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Uno de los requisitos que deben cumplirse es que las variables se encuentran altamente intercorrelacionadas. También se espera que las variables que tengan correlación muy alta entre sí la tengan con el mismo factor o factores. En consecuencia, si las correlaciones entre todas las variables son bajas, tal vez no sea apropiado el Análisis Factorial.
UVWES1 | UVWES4 | UVWES8 | UVWES12 | UVWES15 | UVWES17 | |
---|---|---|---|---|---|---|
Min. :2.00 | Min. :2.00 | Min. :2.0 | Min. :0.00 | Min. :0.00 | Min. :1.00 | |
1st Qu.:3.00 | 1st Qu.:4.00 | 1st Qu.:4.0 | 1st Qu.:4.00 | 1st Qu.:4.00 | 1st Qu.:3.25 | |
Median :4.00 | Median :5.00 | Median :4.0 | Median :4.00 | Median :5.00 | Median :4.00 | |
Mean :4.26 | Mean :4.48 | Mean :4.3 | Mean :4.28 | Mean :4.54 | Mean :4.24 | |
3rd Qu.:5.00 | 3rd Qu.:5.00 | 3rd Qu.:5.0 | 3rd Qu.:5.00 | 3rd Qu.:5.00 | 3rd Qu.:5.00 | |
Max. :6.00 | Max. :6.00 | Max. :6.0 | Max. :6.00 | Max. :6.00 | Max. :6.00 | |
### E | stadisticos de | los elementos: | absorción |
UVWES3 | UVWES6 | UVWES9 | UVWES11 | UVWES14 | UVWES16 | |
---|---|---|---|---|---|---|
Min. :2.00 | Min. :0.00 | Min. :2.00 | Min. :2.00 | Min. :2.00 | Min. :0.00 | |
1st Qu.:4.00 | 1st Qu.:4.00 | 1st Qu.:3.00 | 1st Qu.:4.00 | 1st Qu.:4.00 | 1st Qu.:3.25 | |
Median :4.50 | Median :4.00 | Median :4.00 | Median :4.00 | Median :4.00 | Median :4.00 | |
Mean :4.38 | Mean :4.06 | Mean :4.26 | Mean :4.42 | Mean :4.26 | Mean :4.02 | |
3rd Qu.:5.00 | 3rd Qu.:5.00 | 3rd Qu.:5.00 | 3rd Qu.:5.00 | 3rd Qu.:5.00 | 3rd Qu.:5.00 | |
Max. :6.00 | Max. :6.00 | Max. :6.00 | Max. :6.00 | Max. :6.00 | Max. :6.00 |
UVWES2 | UVWES5 | UVWES7 | UVWES10 | UVWES13 | |
---|---|---|---|---|---|
Min. :2.00 | Min. :2.00 | Min. :2.00 | Min. :2.00 | Min. :1.00 | |
1st Qu.:4.00 | 1st Qu.:4.00 | 1st Qu.:4.00 | 1st Qu.:4.00 | 1st Qu.:3.25 | |
Median :5.00 | Median :5.00 | Median :5.00 | Median :5.00 | Median :4.50 | |
Mean :4.64 | Mean :4.56 | Mean :4.56 | Mean :4.76 | Mean :4.34 | |
3rd Qu.:5.00 | 3rd Qu.:5.00 | 3rd Qu.:5.00 | 3rd Qu.:6.00 | 3rd Qu.:5.00 | |
Max. :6.00 | Max. :6.00 | Max. :6.00 | Max. :6.00 | Max. :6.00 |
SL1 | SL2 | SL3 | SL4 | |
---|---|---|---|---|
Min. :2.00 | Min. :1.00 | Min. :1.00 | Min. :1.00 | |
1st Qu.:4.00 | 1st Qu.:4.00 | 1st Qu.:3.00 | 1st Qu.:3.00 | |
Median :5.00 | Median :5.00 | Median :4.00 | Median :4.00 | |
Mean :5.02 | Mean :4.26 | Mean :4.12 | Mean :4.14 | |
3rd Qu.:6.00 | 3rd Qu.:5.00 | 3rd Qu.:5.00 | 3rd Qu.:5.00 | |
Max. :7.00 | Max. :7.00 | Max. :7.00 | Max. :7.00 |
SL5 | SL6 | SL7 | SL8 | SL9 | SL10 | |
---|---|---|---|---|---|---|
Min. :2.00 | Min. :2.00 | Min. :2.00 | Min. :2.00 | Min. :2.00 | Min. :2.00 | |
1st Qu.:4.00 | 1st Qu.:4.00 | 1st Qu.:4.00 | 1st Qu.:4.00 | 1st Qu.:4.00 | 1st Qu.:4.00 | |
Median :5.00 | Median :4.00 | Median :4.50 | Median :4.00 | Median :4.00 | Median :5.00 | |
Mean :4.84 | Mean :4.72 | Mean :4.58 | Mean :4.52 | Mean :4.46 | Mean :4.84 | |
3rd Qu.:6.00 | 3rd Qu.:6.00 | 3rd Qu.:5.75 | 3rd Qu.:5.75 | 3rd Qu.:5.00 | 3rd Qu.:6.00 | |
Max. :7.00 | Max. :7.00 | Max. :7.00 | Max. :7.00 | Max. :7.00 | Max. :7.00 |
SL11 | SL12 | |
---|---|---|
Min. :2.00 | Min. :1.00 | |
1st Qu.:4.00 | 1st Qu.:4.00 | |
Median :5.00 | Median :4.00 | |
Mean :4.56 | Mean :4.44 | |
3rd Qu.:5.00 | 3rd Qu.:5.00 | |
Max. :7.00 | Max. :7.00 |
Alfa de Cronbach y consistencia interna de los ítems de un instrumento de medida El método de consistencia interna basado en el alfa de Cronbach permite estimar la fiabilidad de un instrumento de medida a través de un conjunto de ítems que se espera que midan el mismo constructo o dimensión teórica.
La validez de un instrumento se refiere al grado en que el instrumento mide aquello que pretende medir. Y la fiabilidad de la consistencia interna del instrumento se puede estimar con el alfa de Cronbach. La medida de la fiabilidad mediante el alfa de Cronbach asume que los ítems (medidos en escala tipo Likert) miden un mismo constructo y que están altamente correlacionados (Welch & Comer, 1988). Cuanto más cerca se encuentre el valor del alfa a 1 mayor es la consistencia interna de los ítems analizados. La fiabilidad de la escala debe obtenerse siempre con los datos de cada muestra para garantizar la medida fiable del constructo en la muestra concreta de investigación. Como criterio general, George y Mallery (2003, p. 231) sugieren las recomendaciones siguientes para evaluar los coeficientes de alfa de Cronbach:
Coeficiente alfa >.9 es excelente
Coeficiente alfa >.8 es bueno
Coeficiente alfa >.7 es aceptable
Coeficiente alfa >.6 es cuestionable
Coeficiente alfa >.5 es pobre
Coeficiente alfa <.5 es inaceptable
Reliability analysis
Call: alpha(x = vigor)
raw_alpha std.alpha G6(smc) average_r S/N ase mean sd
0.84 0.84 0.84 0.47 5.3 0.036 4.3 0.84
lower alpha upper 95% confidence boundaries
0.77 0.84 0.91
Reliability if an item is dropped:
raw_alpha std.alpha G6(smc) average_r S/N alpha se NA
UVWES1 0.79 0.80 0.77 0.44 3.9 0.046 0.007
UVWES4 0.79 0.80 0.78 0.44 3.9 0.046 0.010
UVWES8 0.83 0.84 0.82 0.50 5.1 0.039 0.011
UVWES12 0.82 0.82 0.81 0.48 4.7 0.040 0.011
UVWES15 0.81 0.81 0.79 0.46 4.2 0.043 0.009
UVWES17 0.83 0.83 0.81 0.49 4.8 0.039 0.014
Item statistics
n raw.r std.r r.cor r.drop mean sd
UVWES1 50 0.81 0.81 0.79 0.71 4.3 1.12
UVWES4 50 0.81 0.81 0.78 0.72 4.5 0.99
UVWES8 50 0.66 0.67 0.56 0.51 4.3 1.05
UVWES12 50 0.72 0.71 0.64 0.57 4.3 1.21
UVWES15 50 0.77 0.77 0.72 0.64 4.5 1.20
UVWES17 50 0.71 0.70 0.60 0.55 4.2 1.20
Non missing response frequency for each item
0 1 2 3 4 5 6 miss
UVWES1 0.00 0.00 0.06 0.22 0.24 0.36 0.12 0
UVWES4 0.00 0.00 0.02 0.18 0.22 0.46 0.12 0
UVWES8 0.00 0.00 0.06 0.16 0.30 0.38 0.10 0
UVWES12 0.02 0.00 0.04 0.16 0.32 0.32 0.14 0
UVWES15 0.02 0.00 0.04 0.04 0.38 0.30 0.22 0
UVWES17 0.00 0.02 0.04 0.20 0.34 0.22 0.18 0
Reliability analysis
Call: alpha(x = absorcion)
raw_alpha std.alpha G6(smc) average_r S/N ase mean sd
0.72 0.74 0.75 0.32 2.8 0.062 4.2 0.76
lower alpha upper 95% confidence boundaries
0.6 0.72 0.84
Reliability if an item is dropped:
raw_alpha std.alpha G6(smc) average_r S/N alpha se NA
UVWES3 0.68 0.70 0.70 0.32 2.4 0.073 0.028
UVWES6 0.70 0.73 0.72 0.35 2.6 0.068 0.028
UVWES9 0.67 0.69 0.69 0.31 2.3 0.074 0.023
UVWES11 0.63 0.63 0.62 0.26 1.7 0.084 0.017
UVWES14 0.67 0.69 0.68 0.31 2.2 0.074 0.019
UVWES16 0.74 0.75 0.76 0.38 3.1 0.059 0.025
Item statistics
n raw.r std.r r.cor r.drop mean sd
UVWES3 50 0.67 0.66 0.56 0.46 4.4 1.26
UVWES6 50 0.61 0.60 0.47 0.40 4.1 1.22
UVWES9 50 0.67 0.68 0.61 0.49 4.3 1.14
UVWES11 50 0.80 0.82 0.82 0.70 4.4 0.95
UVWES14 50 0.67 0.69 0.64 0.50 4.3 1.12
UVWES16 50 0.54 0.51 0.32 0.28 4.0 1.32
Non missing response frequency for each item
0 1 2 3 4 5 6 miss
UVWES3 0.00 0.00 0.10 0.14 0.26 0.28 0.22 0
UVWES6 0.02 0.02 0.06 0.14 0.36 0.34 0.06 0
UVWES9 0.00 0.00 0.06 0.22 0.26 0.32 0.14 0
UVWES11 0.00 0.00 0.02 0.14 0.36 0.36 0.12 0
UVWES14 0.00 0.00 0.06 0.18 0.36 0.24 0.16 0
UVWES16 0.02 0.04 0.06 0.14 0.34 0.32 0.08 0
Reliability analysis
Call: alpha(x = dedicacion)
raw_alpha std.alpha G6(smc) average_r S/N ase mean sd
0.79 0.78 0.78 0.42 3.6 0.047 4.6 0.77
lower alpha upper 95% confidence boundaries
0.7 0.79 0.88
Reliability if an item is dropped:
raw_alpha std.alpha G6(smc) average_r S/N alpha se NA
UVWES2 0.77 0.77 0.75 0.45 3.3 0.050 0.0197
UVWES5 0.78 0.78 0.75 0.47 3.6 0.051 0.0071
UVWES7 0.75 0.75 0.71 0.42 2.9 0.056 0.0186
UVWES10 0.72 0.72 0.71 0.39 2.5 0.064 0.0269
UVWES13 0.70 0.70 0.69 0.37 2.4 0.069 0.0258
Item statistics
n raw.r std.r r.cor r.drop mean sd
UVWES2 50 0.67 0.68 0.57 0.48 4.6 1.03
UVWES5 50 0.65 0.65 0.54 0.46 4.6 0.97
UVWES7 50 0.72 0.73 0.66 0.56 4.6 0.93
UVWES10 50 0.79 0.79 0.73 0.65 4.8 1.08
UVWES13 50 0.83 0.81 0.76 0.68 4.3 1.22
Non missing response frequency for each item
1 2 3 4 5 6 miss
UVWES2 0.00 0.04 0.10 0.22 0.46 0.18 0
UVWES5 0.00 0.02 0.12 0.30 0.40 0.16 0
UVWES7 0.00 0.02 0.10 0.32 0.42 0.14 0
UVWES10 0.00 0.02 0.12 0.24 0.32 0.30 0
UVWES13 0.02 0.04 0.20 0.24 0.32 0.18 0
Reliability analysis
Call: alpha(x = satisfacionAmbienteFis)
raw_alpha std.alpha G6(smc) average_r S/N ase mean sd
0.78 0.77 0.78 0.46 3.4 0.051 4.4 1.1
lower alpha upper 95% confidence boundaries
0.68 0.78 0.88
Reliability if an item is dropped:
raw_alpha std.alpha G6(smc) average_r S/N alpha se NA
SL1 0.82 0.83 0.81 0.61 4.8 0.045 0.0249
SL2 0.66 0.65 0.60 0.38 1.8 0.082 0.0333
SL3 0.62 0.62 0.53 0.35 1.6 0.092 0.0084
SL4 0.75 0.74 0.73 0.48 2.8 0.061 0.0582
Item statistics
n raw.r std.r r.cor r.drop mean sd
SL1 50 0.58 0.62 0.38 0.35 5.0 1.2
SL2 50 0.85 0.84 0.83 0.70 4.3 1.4
SL3 50 0.88 0.87 0.89 0.77 4.1 1.4
SL4 50 0.76 0.74 0.62 0.54 4.1 1.4
Non missing response frequency for each item
1 2 3 4 5 6 7 miss
SL1 0.00 0.02 0.10 0.16 0.38 0.24 0.10 0
SL2 0.08 0.06 0.06 0.28 0.38 0.12 0.02 0
SL3 0.04 0.10 0.16 0.24 0.34 0.10 0.02 0
SL4 0.04 0.12 0.16 0.20 0.32 0.14 0.02 0
Reliability analysis
Call: alpha(x = satisfacionSupervision)
raw_alpha std.alpha G6(smc) average_r S/N ase mean sd
0.95 0.95 0.96 0.76 19 0.011 4.7 1.2
lower alpha upper 95% confidence boundaries
0.93 0.95 0.97
Reliability if an item is dropped:
raw_alpha std.alpha G6(smc) average_r S/N alpha se NA
SL5 0.94 0.94 0.95 0.76 16 0.014 0.0057
SL6 0.94 0.94 0.94 0.76 16 0.014 0.0036
SL7 0.94 0.94 0.94 0.75 15 0.014 0.0029
SL8 0.94 0.94 0.94 0.76 16 0.014 0.0045
SL9 0.94 0.94 0.94 0.77 17 0.013 0.0038
SL10 0.94 0.94 0.94 0.76 16 0.013 0.0038
Item statistics
n raw.r std.r r.cor r.drop mean sd
SL5 50 0.90 0.90 0.88 0.86 4.8 1.4
SL6 50 0.90 0.89 0.87 0.84 4.7 1.5
SL7 50 0.91 0.91 0.91 0.87 4.6 1.3
SL8 50 0.89 0.90 0.88 0.85 4.5 1.2
SL9 50 0.87 0.87 0.85 0.82 4.5 1.3
SL10 50 0.89 0.89 0.87 0.84 4.8 1.4
Non missing response frequency for each item
2 3 4 5 6 7 miss
SL5 0.08 0.06 0.30 0.18 0.26 0.12 0
SL6 0.08 0.06 0.40 0.14 0.16 0.16 0
SL7 0.06 0.12 0.32 0.24 0.20 0.06 0
SL8 0.06 0.10 0.40 0.18 0.22 0.04 0
SL9 0.06 0.18 0.28 0.24 0.20 0.04 0
SL10 0.02 0.16 0.28 0.20 0.18 0.16 0
Reliability analysis
Call: alpha(x = satisfacionPresta)
raw_alpha std.alpha G6(smc) average_r S/N ase mean sd
0.85 0.85 0.74 0.74 5.6 0.043 4.5 1.1
lower alpha upper 95% confidence boundaries
0.76 0.85 0.93
Reliability if an item is dropped:
raw_alpha std.alpha G6(smc) average_r S/N alpha se NA
SL11 0.74 0.74 0.54 0.74 NA NA 0.74
SL12 0.74 0.54 0.74 NA NA NA 0.74
Item statistics
n raw.r std.r r.cor r.drop mean sd
SL11 50 0.93 0.93 0.8 0.74 4.6 1.2
SL12 50 0.93 0.93 0.8 0.74 4.4 1.2
Non missing response frequency for each item
1 2 3 4 5 6 7 miss
SL11 0.00 0.04 0.16 0.28 0.32 0.12 0.08 0
SL12 0.02 0.02 0.16 0.32 0.30 0.14 0.04 0
El test de Kaiser-Meyer-Olkin (KMO), que mide la idoneidad de los datos para realizar un análisis factorial comparando los valores de los coeficientes de correlación observados con los coeficientes de correlación parcial. Si la suma de los cuadrados de los coeficientes de correlación parcial entre todos los pares de variables es pequeña en comparación con la suma de los coeficientes de correlación al cuadrado, esta medida tiende a uno. Para Kaiser (1974 en Visauta, 1998) los resultados del modelo factorial serán excelentes si el índice KMO está comprendido entre 0,9 y 1; buenos, si está comprendido entre 0,8 y 0,9; aceptables, si se encuentra entre 0,7 y 0,8; mediocres o regulares, cuando resulte entre 0,6 y 0,7; malos, si está entre 0,5 y 0,6; e inaceptables o muy malos cuando sea menor que 0,5.
Kaiser-Meyer-Olkin factor adequacy
Call: KMO(r = vigor)
Overall MSA = 0.82
MSA for each item =
UVWES1 UVWES4 UVWES8 UVWES12 UVWES15 UVWES17
0.78 0.86 0.89 0.80 0.81 0.81
Kaiser-Meyer-Olkin factor adequacy
Call: KMO(r = absorcion)
Overall MSA = 0.74
MSA for each item =
UVWES3 UVWES6 UVWES9 UVWES11 UVWES14 UVWES16
0.72 0.73 0.77 0.73 0.72 0.90
Kaiser-Meyer-Olkin factor adequacy
Call: KMO(r = dedicacion)
Overall MSA = 0.73
MSA for each item =
UVWES2 UVWES5 UVWES7 UVWES10 UVWES13
0.75 0.67 0.68 0.77 0.77
Kaiser-Meyer-Olkin factor adequacy
Call: KMO(r = satisfacionAmbienteFis)
Overall MSA = 0.63
MSA for each item =
SL1 SL2 SL3 SL4
0.78 0.61 0.59 0.70
Kaiser-Meyer-Olkin factor adequacy
Call: KMO(r = satisfacionSupervision)
Overall MSA = 0.87
MSA for each item =
SL5 SL6 SL7 SL8 SL9 SL10
0.91 0.89 0.83 0.89 0.87 0.83
Kaiser-Meyer-Olkin factor adequacy
Call: KMO(r = satisfacionPresta)
Overall MSA = 0.5
MSA for each item =
SL11 SL12
0.5 0.5
El test de esfericidad de Barlett, que permite contrastar la hipótesis de que la matriz de correlaciones es una matriz identidad. Si esta hipótesis se aceptase (valor del test bajo y asociado a un nivel de significación alto), se debería cuestionar la utilización de cualquier tipo de análisis factorial, ya que significaría la práctica inexistencia de correlación entre los ítemes. Valores de p menores a 0.05 aceptan la hipotesis nula
Test statistic | df | P value |
---|---|---|
17.12 | 16 | 0.3779 |
Test statistic | df | P value |
---|---|---|
5.849 | 11 | 0.8832 |
El Análisis Factorial es un nombre genérico que se da a una clase de métodos estadísticos multivariantes cuyo propósito principal es definir la estructura subyacente en una matriz de datos. Generalmente hablando, aborda el problema de cómo analizar la estructura de las interrelaciones (correlaciones) entre un gran número de variables.El Análisis Factorial es, por tanto, una técnica de reducción de la dimensionalidad de los datos. Su propósito último consiste en buscar el número mínimo de dimensiones capaces de explicar el máximo de información contenida en los datos.
El Análisis Factorial se encarga de analizar la varianza común a todas las variables. Partiendo de una matriz de correlaciones, trata de simplificar la información que ofrece. Se opera con las correlaciones elevadas al cuadrado r2 (coeficientes de determinación), que expresan la proporción de varianza común entre las variables.
Para iniciar el analisis factorial exploratorio consideremos un analisis simple, sin rotación por el método de “principal axis”. Como inicio seleccionaremos un numero de factores = 5. (El número de factores es seleccionado inicialmente a criterio). Sin embargo lo que queremos es expresar la variación de los datos en el menor número de factores (ejes) segun sea posible.
Considerando la matrix correspondiente a WorkEngagement:
fitFA = fa(WorkEngagement, nfactors = 3, rotate = "none")
examinemos las cargas factoriales
Loadings:
MR1 MR2 MR3
UVWES1 0.819 0.195 -0.278
UVWES2 0.561 0.174 0.204
UVWES3 0.691 0.269 -0.184
UVWES4 0.784 -0.187
UVWES5 0.538 -0.322 -0.249
UVWES6 0.472 0.375
UVWES7 0.615 0.422 0.266
UVWES8 0.548
UVWES9 0.634 -0.304
UVWES10 0.756 -0.236
UVWES11 0.783 -0.142
UVWES12 0.691 -0.409
UVWES13 0.780 -0.233
UVWES14 0.675 -0.249 0.127
UVWES15 0.748 0.435
UVWES16 0.345 0.595
UVWES17 0.576 -0.103 0.237
MR1 MR2 MR3
SS loadings 7.407 1.170 0.819
Proportion Var 0.436 0.069 0.048
Cumulative Var 0.436 0.505 0.553
Las cargas factoriales nos dan una idea de en qué factor carga cada variable. También obtenemos la varianza explicada por cada factor y vemos que con 2 factores se explica el 50,5% de las variabilidad y con 3 el 55.3%.
Ahora examinemos un “scree plot”. Este gráfico nos permite observar los valores propios para poder seleccionar el número de factores.
El grafico del análisis de analisis factorial sin rotación.
Se observa claramente el factor structural , pero las variables que componen los otros dos factores o constructos cargan en el mismo factor. Lo que confirma el análisis de las autocorrelaciones.
Ahora bien, podemos utilizar rotación varimax y seleccionar 5 componentes como nos indica el screeplot
Factor Analysis using method = pa
Call: fa(r = WorkEngagement, nfactors = 5, rotate = "varimax", fm = "pa")
Standardized loadings (pattern matrix) based upon correlation matrix
PA2 PA1 PA5 PA4 PA3 h2 u2 com
UVWES1 0.68 0.42 0.25 0.26 -0.09 0.77 0.23 2.4
UVWES2 0.39 0.17 0.46 0.07 0.20 0.43 0.57 2.7
UVWES3 0.75 0.38 0.02 0.03 0.08 0.71 0.29 1.5
UVWES4 0.50 0.61 0.06 0.24 0.09 0.70 0.30 2.3
UVWES5 0.13 0.52 0.06 0.45 -0.10 0.50 0.50 2.2
UVWES6 0.58 0.06 0.07 0.10 0.15 0.38 0.62 1.3
UVWES7 0.57 -0.07 0.60 0.17 0.23 0.76 0.24 2.5
UVWES8 0.30 0.11 0.06 0.76 0.24 0.74 0.26 1.6
UVWES9 0.06 0.43 0.32 0.59 0.12 0.66 0.34 2.6
UVWES10 0.52 0.42 0.27 0.34 -0.10 0.65 0.35 3.4
UVWES11 0.39 0.66 0.26 0.09 0.18 0.69 0.31 2.2
UVWES12 0.15 0.81 0.09 0.13 0.23 0.76 0.24 1.3
UVWES13 0.25 0.61 0.45 0.20 0.17 0.70 0.30 2.7
UVWES14 0.09 0.55 0.67 0.14 0.07 0.79 0.21 2.1
UVWES15 0.76 0.18 0.27 0.18 0.12 0.73 0.27 1.6
UVWES16 0.08 0.10 0.14 0.09 0.76 0.62 0.38 1.2
UVWES17 0.26 0.41 0.08 0.15 0.46 0.48 0.52 2.9
PA2 PA1 PA5 PA4 PA3
SS loadings 3.35 3.35 1.66 1.56 1.14
Proportion Var 0.20 0.20 0.10 0.09 0.07
Cumulative Var 0.20 0.39 0.49 0.58 0.65
Proportion Explained 0.30 0.30 0.15 0.14 0.10
Cumulative Proportion 0.30 0.61 0.76 0.90 1.00
Mean item complexity = 2.1
Test of the hypothesis that 5 factors are sufficient.
The degrees of freedom for the null model are 136 and the objective function was 12.95 with Chi Square of 550.23
The degrees of freedom for the model are 61 and the objective function was 2.73
The root mean square of the residuals (RMSR) is 0.05
The df corrected root mean square of the residuals is 0.07
The harmonic number of observations is 50 with the empirical chi square 28.71 with prob < 1
The total number of observations was 50 with Likelihood Chi Square = 106.85 with prob < 0.00026
Tucker Lewis Index of factoring reliability = 0.725
RMSEA index = 0.156 and the 90 % confidence intervals are 0.084 0.162
BIC = -131.79
Fit based upon off diagonal values = 0.99
Measures of factor score adequacy
PA2 PA1 PA5 PA4 PA3
Correlation of (regression) scores with factors 0.93 0.92 0.87 0.86 0.84
Multiple R square of scores with factors 0.86 0.85 0.76 0.73 0.70
Minimum correlation of possible factor scores 0.72 0.71 0.53 0.47 0.41
Ahora se observa mejor la estructura de los datos. Esto nos hace pensar a pesar de que tengamos 3 dimensiones (vigor, absorción y dedicación) en realidad al parecer existen 5 dimensiones intrinsicas al dataset. Esto se comprueba tambien con la cantidad de clusters encontrados en el plot de autocorrelación.
Ahora repetimos los analisis para la matriz de satisfacción laboral.
fitSA = fa(SatisfacciónLaboral, nfactors = 3, rotate = "none")
examinemos las cargas factoriales
Loadings:
MR1 MR2 MR3
SL1 0.768 0.301
SL2 0.403 0.751 0.289
SL3 0.555 0.777
SL4 0.402 0.472 -0.273
SL5 0.848 -0.219
SL6 0.873 -0.101
SL7 0.903
SL8 0.859 -0.182
SL9 0.835 -0.195 -0.193
SL10 0.848 -0.186 -0.187
SL11 0.836 -0.243
SL12 0.741 -0.163 0.390
MR1 MR2 MR3
SS loadings 6.921 1.617 0.530
Proportion Var 0.577 0.135 0.044
Cumulative Var 0.577 0.711 0.756
Las cargas factoriales nos dan una idea de en qué factor carga cada variable. También obtenemos la varianza explicada por cada factor y vemos que con 2 factores se explica el 71,1% del total de la varianza y con 3 el 75.6%.
Ahora examinemos un “scree plot”. Este gráfico nos permite observar los valores propios para poder seleccionar el número de factores.
El grafico del análisis de analisis factorial sin rotación.
Se observa claramente el factor structural , pero las variables que componen los otros dos factores o constructos cargan en el mismo factor. Lo que confirma el análisis de las autocorrelaciones.
Ahora bien, podemos utilizar rotación varimax y seleccionar 3 componentes como nos indica el screeplot
Factor Analysis using method = pa
Call: fa(r = SatisfacciónLaboral, nfactors = 3, rotate = "varimax",
fm = "pa")
Standardized loadings (pattern matrix) based upon correlation matrix
PA1 PA2 PA3 h2 u2 com
SL1 0.64 0.17 0.49 0.69 0.313 2.0
SL2 0.00 0.81 0.40 0.82 0.184 1.5
SL3 0.22 0.93 0.08 0.91 0.089 1.1
SL4 0.24 0.62 -0.15 0.46 0.537 1.4
SL5 0.85 0.11 0.17 0.77 0.230 1.1
SL6 0.79 0.22 0.32 0.78 0.219 1.5
SL7 0.80 0.38 0.17 0.82 0.177 1.5
SL8 0.80 0.35 0.05 0.77 0.228 1.4
SL9 0.87 0.15 0.03 0.77 0.227 1.1
SL10 0.87 0.16 0.04 0.79 0.212 1.1
SL11 0.83 0.08 0.24 0.76 0.242 1.2
SL12 0.63 0.08 0.57 0.73 0.274 2.0
PA1 PA2 PA3
SS loadings 5.78 2.31 0.98
Proportion Var 0.48 0.19 0.08
Cumulative Var 0.48 0.67 0.76
Proportion Explained 0.64 0.26 0.11
Cumulative Proportion 0.64 0.89 1.00
Mean item complexity = 1.4
Test of the hypothesis that 3 factors are sufficient.
The degrees of freedom for the null model are 66 and the objective function was 12.38 with Chi Square of 546.59
The degrees of freedom for the model are 33 and the objective function was 1.64
The root mean square of the residuals (RMSR) is 0.04
The df corrected root mean square of the residuals is 0.05
The harmonic number of observations is 50 with the empirical chi square 8.95 with prob < 1
The total number of observations was 50 with Likelihood Chi Square = 69.24 with prob < 0.00022
Tucker Lewis Index of factoring reliability = 0.841
RMSEA index = 0.171 and the 90 % confidence intervals are 0.1 0.199
BIC = -59.86
Fit based upon off diagonal values = 1
Measures of factor score adequacy
PA1 PA2 PA3
Correlation of (regression) scores with factors 0.97 0.97 0.84
Multiple R square of scores with factors 0.94 0.94 0.71
Minimum correlation of possible factor scores 0.89 0.88 0.41
Ahora se observa mejor la estructura de los datos. Esto nos hace pensar a pesar de que tengamos 3 dimensiones (Satisfacción Ambiente Fisico, Satisfacción Supervisión y Satisfacción Prestaciones) en realidad al parecer unicamente25 dimensiones intrinsicas al dataset. Esto se comprueba tambien con la cantidad de clusters encontrados en el plot de autocorrelación. (2 clusters definidos). Repitamos el analisis unicamente seleccionando 2 factores.
The estimated weights for the factor scores are probably incorrect. Try a different factor extraction method.
Factor Analysis using method = pa
Call: fa(r = SatisfacciónLaboral, nfactors = 2, rotate = "varimax",
fm = "pa")
Standardized loadings (pattern matrix) based upon correlation matrix
PA1 PA2 h2 u2 com
SL1 0.73 0.21 0.58 0.418 1.2
SL2 0.11 0.76 0.59 0.413 1.0
SL3 0.20 1.00 1.04 -0.036 1.1
SL4 0.19 0.57 0.36 0.637 1.2
SL5 0.87 0.12 0.78 0.224 1.0
SL6 0.85 0.24 0.78 0.224 1.2
SL7 0.82 0.39 0.82 0.177 1.4
SL8 0.78 0.35 0.74 0.264 1.4
SL9 0.84 0.14 0.73 0.272 1.1
SL10 0.85 0.15 0.75 0.252 1.1
SL11 0.87 0.10 0.76 0.239 1.0
SL12 0.73 0.14 0.55 0.454 1.1
PA1 PA2
SS loadings 6.10 2.36
Proportion Var 0.51 0.20
Cumulative Var 0.51 0.71
Proportion Explained 0.72 0.28
Cumulative Proportion 0.72 1.00
Mean item complexity = 1.1
Test of the hypothesis that 2 factors are sufficient.
The degrees of freedom for the null model are 66 and the objective function was 12.38 with Chi Square of 546.59
The degrees of freedom for the model are 43 and the objective function was 2.23
The root mean square of the residuals (RMSR) is 0.05
The df corrected root mean square of the residuals is 0.07
The harmonic number of observations is 50 with the empirical chi square 19.58 with prob < 1
The total number of observations was 50 with Likelihood Chi Square = 95.53 with prob < 7.3e-06
Tucker Lewis Index of factoring reliability = 0.826
RMSEA index = 0.177 and the 90 % confidence intervals are 0.115 0.201
BIC = -72.69
Fit based upon off diagonal values = 0.99
Aqui se observa mas claramente como el dataset de satisfacción laboral esta estructurado. Se puede observar que muchas de las preguntas respecto a Satisfacción Ambiente Fisico estan correlacionadas con las de Satisfacción de la Supervisión.
Si hay ‘n’ factores, se interpreta que el instrumento original se puede descomponer en ‘n’ instrumentos (cada uno compuesto por todos los ítems), aunque en cada instrumento los ítems tienen un ‘peso específico’ distinto según sea su relación con el factor:
Si encontramos, por ejemplo, tres factores, esto quiere decir que podemos descomponer el instrumento original en tres instrumentos; cada uno está compuesto por todos los ítems, pero en cada instrumento los ítems tienen un peso específico distinto según sea su relación con cada factor.
Los pesos pueden ser grandes o pequeños, positivos o negativos. Generalmente, en cada factor hay ítems con pesos grandes y otros próximos a cero; los ítems que más pesan en cada factor son los que lo definen. La varianza (diversidad) de todas las nuevas medidas equivale a la varianza de la medida original (no a toda, pero sí a la máxima que es posible explicar); estos factores indican las fuentes de varianza; si hay diferencias en la medida original es porque las hay en estas nuevas puntuaciones.
Histogramas representando la distribución de la varianza en los dos primeros factores en cada caso
El Maximun Likelihood Factor Analysis (maxima verosimilidad) Basado en el modelo x = A f + u <-> X = FA’ + U, adoptando la hipótesis de normalidad multivariante, aplica el método de la máxima verosimilitud. Sobre los anteriores, tiene la ventaja de que las estimaciones obtenidas no dependen de la escala de medida de las variables. Por otra parte, como está basado en el método de máxima verosimilitud, tiene todas las propiedades estadísticas de éste y, en particular, es asintóticamente insesgada, eficiente y normal si las hipótesis del modelo factorial son ciertas. Además, permite seleccionar el número de factores mediante contrastes de hipótesis.
Call:
factanal(x = WorkEngagement, factors = 5, scores = "regression", rotation = "varimax")
Uniquenesses:
UVWES1 UVWES2 UVWES3 UVWES4 UVWES5 UVWES6 UVWES7 UVWES8 UVWES9
0.22 0.57 0.31 0.00 0.59 0.52 0.23 0.71 0.52
UVWES10 UVWES11 UVWES12 UVWES13 UVWES14 UVWES15 UVWES16 UVWES17
0.36 0.27 0.01 0.26 0.24 0.32 0.00 0.61
Loadings:
Factor1 Factor2 Factor3 Factor4 Factor5
UVWES1 0.67 0.31 0.38
UVWES3 0.59 0.53
UVWES6 0.66
UVWES7 0.71 0.41
UVWES15 0.71 0.33
UVWES9 0.55 0.32
UVWES13 0.63 0.39
UVWES14 0.79
UVWES4 0.89
UVWES5 0.34 0.50
UVWES11 0.41 0.39 0.57
UVWES12 0.35 0.87
UVWES16 0.98
UVWES2 0.50 0.40
UVWES8 0.37
UVWES10 0.47 0.42 0.47
UVWES17 0.30 0.35
Factor1 Factor2 Factor3 Factor4 Factor5
SS loadings 3.30 2.52 2.31 1.74 1.38
Proportion Var 0.19 0.15 0.14 0.10 0.08
Cumulative Var 0.19 0.34 0.48 0.58 0.66
Test of the hypothesis that 5 factors are sufficient.
The chi square statistic is 93.71 on 61 degrees of freedom.
The p-value is 0.00451
Las influencias cercanas a -1 o 1 indican que el factor afecta considerablemente a la variable. Las influencias cercanas a 0 indican que el factor tiene poca influencia en la variable. Algunas variables pueden tener grandes influencias en múltiples factores.
UVWES15, UVWES7, UVWES1, UVWES6 son las variables que mas contribuyen en el factor 1 de WorkEngagement.
UVWES3, UVWES14, UVWES13 son las variables que mas contribuyen en el factor 2 de WorkEngagement.
UVWES3, UVWES4 son las variables que mas contribuyen en el factor 3 de WorkEngagement.
UVWES11 son las variables que mas contribuyen en el factor 4 de WorkEngagement.
UVWES16 son las variables que mas contribuyen en el factor 5 de WorkEngagement.
En conjunto los 5 factores explican lel 66% de la variación en los datos.
Usemos un grafico de influencias para visualizar las influencias de las variables sobre los dos primeros factores
Como se puede observar, usando todas las variables todavia se obtienen demasiadas dimensiones para tener un análisis safifactorio y claro. En la grafica tambien se puede observar que muchas variables tienen similares cargas y dirección sobre los factores. Esto junto a los analisis de autocorrelación anteriores nos indican que tal ves seria conviente eliminar items para reducir la variación de los datos y llegar a una conclusión más clara.
De la matrix de autocorrelación seleccionemos unicamente los que presentan valores de autocorrelación mayores a 0.6 (para visualizar se ha reemplazado los valores menores a 0.6 con 0)
UVWES1 UVWES2 UVWES3 UVWES4 UVWES5 UVWES6 UVWES7
UVWES1 1.0000000 0 0.6653178 0.6359714 0 0 0.0000000
UVWES2 0.0000000 1 0.0000000 0.0000000 0 0 0.0000000
UVWES3 0.6653178 0 1.0000000 0.6982959 0 0 0.0000000
UVWES4 0.6359714 0 0.6982959 1.0000000 0 0 0.0000000
UVWES5 0.0000000 0 0.0000000 0.0000000 1 0 0.0000000
UVWES6 0.0000000 0 0.0000000 0.0000000 0 1 0.0000000
UVWES7 0.0000000 0 0.0000000 0.0000000 0 0 1.0000000
UVWES8 0.0000000 0 0.0000000 0.0000000 0 0 0.0000000
UVWES9 0.0000000 0 0.0000000 0.0000000 0 0 0.0000000
UVWES10 0.0000000 0 0.0000000 0.6605480 0 0 0.0000000
UVWES11 0.6811515 0 0.0000000 0.0000000 0 0 0.0000000
UVWES12 0.0000000 0 0.0000000 0.0000000 0 0 0.0000000
UVWES13 0.0000000 0 0.0000000 0.6519031 0 0 0.0000000
UVWES14 0.0000000 0 0.0000000 0.0000000 0 0 0.0000000
UVWES15 0.6676462 0 0.6045246 0.0000000 0 0 0.6206154
UVWES16 0.0000000 0 0.0000000 0.0000000 0 0 0.0000000
UVWES17 0.0000000 0 0.0000000 0.0000000 0 0 0.0000000
UVWES8 UVWES9 UVWES10 UVWES11 UVWES12 UVWES13
UVWES1 0.0000000 0.0000000 0.0000000 0.6811515 0.0000000 0.0000000
UVWES2 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
UVWES3 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
UVWES4 0.0000000 0.0000000 0.6605480 0.0000000 0.0000000 0.6519031
UVWES5 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
UVWES6 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
UVWES7 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
UVWES8 1.0000000 0.6130729 0.0000000 0.0000000 0.0000000 0.0000000
UVWES9 0.6130729 1.0000000 0.0000000 0.0000000 0.0000000 0.0000000
UVWES10 0.0000000 0.0000000 1.0000000 0.0000000 0.0000000 0.0000000
UVWES11 0.0000000 0.0000000 0.0000000 1.0000000 0.7641146 0.0000000
UVWES12 0.0000000 0.0000000 0.0000000 0.7641146 1.0000000 0.6364958
UVWES13 0.0000000 0.0000000 0.0000000 0.0000000 0.6364958 1.0000000
UVWES14 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.7232389
UVWES15 0.0000000 0.0000000 0.6855631 0.0000000 0.0000000 0.0000000
UVWES16 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
UVWES17 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
UVWES14 UVWES15 UVWES16 UVWES17
UVWES1 0.0000000 0.6676462 0 0
UVWES2 0.0000000 0.0000000 0 0
UVWES3 0.0000000 0.6045246 0 0
UVWES4 0.0000000 0.0000000 0 0
UVWES5 0.0000000 0.0000000 0 0
UVWES6 0.0000000 0.0000000 0 0
UVWES7 0.0000000 0.6206154 0 0
UVWES8 0.0000000 0.0000000 0 0
UVWES9 0.0000000 0.0000000 0 0
UVWES10 0.0000000 0.6855631 0 0
UVWES11 0.0000000 0.0000000 0 0
UVWES12 0.0000000 0.0000000 0 0
UVWES13 0.7232389 0.0000000 0 0
UVWES14 1.0000000 0.0000000 0 0
UVWES15 0.0000000 1.0000000 0 0
UVWES16 0.0000000 0.0000000 1 0
UVWES17 0.0000000 0.0000000 0 1
Por medio de las autocorrelaciones podemos seleccionar los siguientes candidatos
UVWES12 : UVWES11 = 0.7641146 UVWES13 : UVWES14 = 0.7232389 UVWES1 : UVWES11 = 0.6811515 VWES10 : UVWES15 = 0.6855631 UVWES1 : UVWES15 = 0.6676462 UVWES4 : UVWES10 = 0.6605480
Ahora examinemos las cargas de los factores
Call:
factanal(x = WorkEngagement, factors = 5, scores = "regression", rotation = "varimax")
Uniquenesses:
UVWES1 UVWES2 UVWES3 UVWES4 UVWES5 UVWES6 UVWES7 UVWES8 UVWES9
0.216 0.572 0.308 0.005 0.592 0.516 0.233 0.711 0.521
UVWES10 UVWES11 UVWES12 UVWES13 UVWES14 UVWES15 UVWES16 UVWES17
0.361 0.271 0.014 0.264 0.243 0.317 0.005 0.605
Loadings:
Factor1 Factor2 Factor3 Factor4 Factor5
UVWES1 0.670 0.308 0.379 0.288 -0.120
UVWES2 0.497 0.396 0.141
UVWES3 0.592 0.528 0.245
UVWES4 0.286 0.233 0.891 0.191 0.170
UVWES5 0.337 0.501 0.201
UVWES6 0.659 0.192
UVWES7 0.712 0.409 -0.156 0.260
UVWES8 0.373 0.225 0.214 0.108 0.206
UVWES9 0.184 0.551 0.171 0.324
UVWES10 0.467 0.418 0.470 0.130
UVWES11 0.410 0.389 0.280 0.568
UVWES12 0.110 0.345 0.274 0.871 0.143
UVWES13 0.227 0.628 0.388 0.289 0.237
UVWES14 0.167 0.792 0.229 0.208
UVWES15 0.710 0.234 0.326 0.110
UVWES16 0.128 0.102 0.979
UVWES17 0.248 0.208 0.274 0.301 0.352
Factor1 Factor2 Factor3 Factor4 Factor5
SS loadings 3.304 2.518 2.307 1.736 1.379
Proportion Var 0.194 0.148 0.136 0.102 0.081
Cumulative Var 0.194 0.343 0.478 0.580 0.661
Test of the hypothesis that 5 factors are sufficient.
The chi square statistic is 93.71 on 61 degrees of freedom.
The p-value is 0.00451
Para cada caso de las autocorrelaciones:
UVWES12 : UVWES11 = 0.7641146
UVWES12 se expresa casi unicamente en el factor 4, siendo casi la unica variable que conforma ese factor. Por otro lado UVWES11 tiene su varianza dividida entre los factores 1:4. Esto nos sugiere que para reducir dimensiones probablemente es conveniente eliminar UVWES11.
UVWES13 : UVWES14 = 0.7232389. Estos dos items se expresan mayoritariamente en el factor 2. Sin embargo el UVWES14 tiene una mayor carga. Eliminar UVWES13 seria mas conveniente en este caso.
UVWES1 : UVWES11 = 0.6811515: UVWES1 tiene una mayor carga en el factor 1. UVWESS 11 tiene su varianza repartida entre varios factores del 1:4. Se recomienda eliminar UVWES11.
VWES10 : UVWES15 = 0.6855631: UVWES15 tiene una carga mayoritaria en el factor 1. de lo contrario UVWES10 tiene repartida su carga entre varios factores. Se recomienda eliminar UVWES10
UVWES1 : UVWES15 = 0.6676462: Mismo caso anterior. Se recomienda eliminar UVWES1
UVWES4 : UVWES10 = 0.6605480: Se habia recomendado eliminar UVEWS 10 anteriormente. Esto se corrobora ya que UVWES 4 tiene la mayoria de varianza en el factor 3.
Solucion candidatos a una eliminación: UVWES11, UVWES13, UVWES10,UVWES1
revisemos como cambian los valores de C.alpha para estos candidatos
Reliability analysis
Call: alpha(x = WorkEngagement)
raw_alpha std.alpha G6(smc) average_r S/N ase mean sd
0.92 0.92 0.96 0.41 12 0.016 4.4 0.75
lower alpha upper 95% confidence boundaries
0.89 0.92 0.95
Reliability if an item is dropped:
raw_alpha std.alpha G6(smc) average_r S/N alpha se NA
UVWES1 0.91 0.91 0.95 0.40 11 0.018 0.022
UVWES2 0.92 0.92 0.96 0.42 12 0.017 0.025
UVWES3 0.91 0.92 0.95 0.41 11 0.018 0.024
UVWES4 0.91 0.91 0.95 0.40 11 0.018 0.023
UVWES5 0.92 0.92 0.96 0.42 12 0.017 0.023
UVWES6 0.92 0.92 0.96 0.43 12 0.016 0.023
UVWES7 0.92 0.92 0.96 0.42 11 0.017 0.024
UVWES8 0.92 0.92 0.96 0.42 12 0.017 0.025
UVWES9 0.92 0.92 0.96 0.41 11 0.017 0.024
UVWES10 0.91 0.92 0.95 0.40 11 0.018 0.023
UVWES11 0.91 0.91 0.95 0.40 11 0.018 0.023
UVWES12 0.91 0.92 0.96 0.41 11 0.018 0.023
UVWES13 0.91 0.91 0.95 0.40 11 0.018 0.023
UVWES14 0.91 0.92 0.96 0.41 11 0.018 0.024
UVWES15 0.91 0.92 0.95 0.41 11 0.018 0.023
UVWES16 0.92 0.93 0.96 0.44 12 0.016 0.020
UVWES17 0.92 0.92 0.96 0.42 11 0.017 0.025
Item statistics
n raw.r std.r r.cor r.drop mean sd
UVWES1 50 0.80 0.80 0.80 0.76 4.3 1.12
UVWES2 50 0.60 0.60 0.58 0.54 4.6 1.03
UVWES3 50 0.70 0.70 0.69 0.65 4.4 1.26
UVWES4 50 0.78 0.79 0.78 0.75 4.5 0.99
UVWES5 50 0.55 0.56 0.54 0.49 4.6 0.97
UVWES6 50 0.52 0.52 0.48 0.45 4.1 1.22
UVWES7 50 0.63 0.64 0.63 0.59 4.6 0.93
UVWES8 50 0.60 0.61 0.58 0.55 4.3 1.05
UVWES9 50 0.66 0.66 0.65 0.61 4.3 1.14
UVWES10 50 0.74 0.75 0.75 0.70 4.8 1.08
UVWES11 50 0.79 0.79 0.79 0.75 4.4 0.95
UVWES12 50 0.70 0.70 0.69 0.65 4.3 1.21
UVWES13 50 0.79 0.79 0.79 0.75 4.3 1.22
UVWES14 50 0.69 0.69 0.68 0.63 4.3 1.12
UVWES15 50 0.75 0.74 0.74 0.70 4.5 1.20
UVWES16 50 0.42 0.41 0.38 0.33 4.0 1.32
UVWES17 50 0.63 0.62 0.59 0.57 4.2 1.20
Non missing response frequency for each item
0 1 2 3 4 5 6 miss
UVWES1 0.00 0.00 0.06 0.22 0.24 0.36 0.12 0
UVWES2 0.00 0.00 0.04 0.10 0.22 0.46 0.18 0
UVWES3 0.00 0.00 0.10 0.14 0.26 0.28 0.22 0
UVWES4 0.00 0.00 0.02 0.18 0.22 0.46 0.12 0
UVWES5 0.00 0.00 0.02 0.12 0.30 0.40 0.16 0
UVWES6 0.02 0.02 0.06 0.14 0.36 0.34 0.06 0
UVWES7 0.00 0.00 0.02 0.10 0.32 0.42 0.14 0
UVWES8 0.00 0.00 0.06 0.16 0.30 0.38 0.10 0
UVWES9 0.00 0.00 0.06 0.22 0.26 0.32 0.14 0
UVWES10 0.00 0.00 0.02 0.12 0.24 0.32 0.30 0
UVWES11 0.00 0.00 0.02 0.14 0.36 0.36 0.12 0
UVWES12 0.02 0.00 0.04 0.16 0.32 0.32 0.14 0
UVWES13 0.00 0.02 0.04 0.20 0.24 0.32 0.18 0
UVWES14 0.00 0.00 0.06 0.18 0.36 0.24 0.16 0
UVWES15 0.02 0.00 0.04 0.04 0.38 0.30 0.22 0
UVWES16 0.02 0.04 0.06 0.14 0.34 0.32 0.08 0
UVWES17 0.00 0.02 0.04 0.20 0.34 0.22 0.18 0
Los valores de alpha no cambian drasticamente cuando estos items son eliminados. Adicionalmente todos los valores de alpha son mayores a 0.9. Esto nos indica que podemos proceder a eliminar los items sin tener efecto en la fiabilidad.
Ahora procedemos a eliminar las variables y repetimos el analisis factorial, podemos probar a reducir las dimensiones de 5 a 2.
Call:
factanal(x = WorkEngagement1, factors = 2, scores = "regression", rotation = "varimax")
Uniquenesses:
UVWES2 UVWES3 UVWES4 UVWES5 UVWES6 UVWES7 UVWES8 UVWES9 UVWES12
0.68 0.48 0.37 0.58 0.61 0.50 0.65 0.50 0.43
UVWES14 UVWES15 UVWES16 UVWES17
0.55 0.23 0.86 0.64
Loadings:
Factor1 Factor2
UVWES4 0.64 0.47
UVWES5 0.65 0.06
UVWES9 0.69 0.18
UVWES12 0.73 0.19
UVWES14 0.61 0.28
UVWES3 0.36 0.62
UVWES6 0.09 0.61
UVWES7 0.16 0.69
UVWES15 0.25 0.84
UVWES2 0.31 0.47
UVWES8 0.47 0.35
UVWES16 0.27 0.25
UVWES17 0.49 0.33
Factor1 Factor2
SS loadings 3.06 2.84
Proportion Var 0.24 0.22
Cumulative Var 0.24 0.45
Test of the hypothesis that 2 factors are sufficient.
The chi square statistic is 91.75 on 53 degrees of freedom.
The p-value is 0.00076
Vemos que el resultado del analisis factorial mejora considerablemente. Ahora solo tenemos 2 dimensiones que en conjunto expresan el 45% de la variación. Comparando con el analisis anterior solamente alcanzabamos a explicar el 34% de la variación con los 2 primeros factores. Adicionalmente, ahora tenemos una clara separación de variables por factores. Con variables claramente cargan al factor 1 y otras variables al factor 2. Sin embargo, todavia se observa que items como UVWES16, UVWES8, UVWES2, UVWES17 todavia aportan poco a las cargas de cada factor. El cargar poco o de similar manera en ambos factores hace que estos items sean variables confusoras para la generacion de los factores. Probemos eliminandolas para examinar si podemos incrementar el porcentaje de variación total explicado por los factores.
Call:
factanal(x = WorkEngagement2, factors = 2, scores = "regression", rotation = "varimax")
Uniquenesses:
UVWES3 UVWES4 UVWES5 UVWES6 UVWES7 UVWES9 UVWES12 UVWES14 UVWES15
0.49 0.29 0.48 0.63 0.58 0.61 0.48 0.60 0.09
Loadings:
Factor1 Factor2
UVWES4 0.72 0.44
UVWES5 0.72
UVWES9 0.59 0.19
UVWES12 0.69 0.20
UVWES14 0.57 0.27
UVWES3 0.45 0.55
UVWES6 0.11 0.60
UVWES7 0.17 0.63
UVWES15 0.24 0.92
Factor1 Factor2
SS loadings 2.49 2.25
Proportion Var 0.28 0.25
Cumulative Var 0.28 0.53
Test of the hypothesis that 2 factors are sufficient.
The chi square statistic is 37.2 on 19 degrees of freedom.
The p-value is 0.00749
Ahora observamos que eliminando los items mencionados anteriormente definitivamente ayuda a incrementar la varianza total acumulada explicada por los dos factores de 45% a 53%. Lo que se encuentra dentro de los limites aceptables. Adicionalmente, podemos observar que los items individuales cargan claramente a un factor u otro. Lo que facilitara posteriores análisis e interpretaciones. Podemos visualizar esto nuevamente.
Se observa un patron mucho mas claro. y se han reducido efectivamente las dimensiones a 2 variables. Estas nuevas variables ( factor 1 y factor 2) reflejan la varianza de sus respectivos items. Adicionalmente ambos Factor tiene representación capturan la varianza en las 3 dimensiones de WorkEngagement. Este vector se puede usar ya para buscar posteriores relaciones calculando los “scores” para cada una de las 50 observaciones (i.e. Generar nuevas variables)
Para el caso de work Engagement tendriamos 2 nuevas variables
$`Work Engagement`
Factor1 Factor2
[1,] 0.4988005219 1.00060043
[2,] 0.5268925384 0.35457589
[3,] 0.8901281107 0.47388178
[4,] 0.5464349718 0.13326692
[5,] -0.2752779122 1.28880943
[6,] -0.4509015259 -0.39784953
[7,] 1.3896023720 0.74821849
[8,] 1.4566554864 0.73062588
[9,] 0.5972757569 0.35258429
[10,] 1.2389203114 0.13068963
[11,] -0.5298791869 -0.16970356
[12,] -1.1702461902 -0.17824089
[13,] 0.3226993336 0.36537519
[14,] -0.2436079174 1.22465052
[15,] 0.4644663961 1.13228745
[16,] -0.0006759351 -0.35778079
[17,] 0.5899619845 0.32298922
[18,] -0.1240593599 0.47086285
[19,] 0.6610422751 -0.37848781
[20,] 0.3860248318 0.37518920
[21,] 0.9914170714 0.84927282
[22,] -0.1939662051 0.54478864
[23,] 0.2138305537 0.50899132
[24,] 0.5142130096 0.28429933
[25,] 0.5899619845 0.32298922
[26,] 0.0185412342 -0.30862024
[27,] 1.3571121643 -1.61734998
[28,] 1.1310701463 0.97327664
[29,] 0.7853654052 0.76145051
[30,] 0.2554468935 1.08568305
[31,] -1.5292094262 -0.11059783
[32,] -0.0686516005 0.03816817
[33,] -0.1019101887 0.52745609
[34,] 0.1340506076 -0.33741814
[35,] -1.4983230379 -0.18102280
[36,] 0.0891880211 -0.44653299
[37,] -0.3751525510 -0.35915965
[38,] -1.4378858352 -0.24126527
[39,] 0.0026805207 1.31691925
[40,] -1.2385327850 -0.41808573
[41,] 1.3726137505 -3.95227595
[42,] 0.6616037554 -2.33129655
[43,] -2.4646355655 0.03382182
[44,] -0.8690672829 -1.13589447
[45,] -1.2747510412 -1.77887403
[46,] -0.7901438232 -0.44151211
[47,] -1.6049584011 -0.14928772
[48,] -0.7247455238 -0.27172375
[49,] -0.3442661627 -0.42958461
[50,] -0.3751525510 -0.35915965
Se realizaron tres rondas de eliminación cuyo efecto y resultados se resumen en la siguiente tabla:
Rondas.de.eliminacion | Statistic | Valor_p | Numero_Factores | Numero.obs | Grados.de.Libertad | Numero.items.incluidos | KMO | Varianza.Acumulada |
---|---|---|---|---|---|---|---|---|
1 | 93.70687 | 0.0045079 | 5 | 50 | 61 | 17 | 0.7881847 | 0.6614700 |
2 | 91.75497 | 0.0007603 | 2 | 50 | 53 | 13 | 0.7411523 | 0.4538821 |
3 | 37.19876 | 0.0074928 | 2 | 50 | 19 | 9 | 0.7543082 | 0.5269698 |
Examinemos ahora el analisis factorial para Satisfacción Laboral.
Call:
factanal(x = SatisfacciónLaboral, factors = 2, scores = "regression", rotation = "varimax")
Uniquenesses:
SL1 SL2 SL3 SL4 SL5 SL6 SL7 SL8 SL9 SL10 SL11 SL12
0.43 0.37 0.00 0.62 0.20 0.21 0.18 0.22 0.29 0.26 0.28 0.47
Loadings:
Factor1 Factor2
SL1 0.74 0.14
SL5 0.89 0.08
SL6 0.86 0.23
SL7 0.83 0.36
SL8 0.79 0.38
SL9 0.83 0.18
SL10 0.84 0.17
SL11 0.83 0.17
SL12 0.71 0.15
SL2 0.09 0.79
SL3 0.20 0.98
SL4 0.20 0.59
Factor1 Factor2
SS loadings 6.08 2.39
Proportion Var 0.51 0.20
Cumulative Var 0.51 0.71
Test of the hypothesis that 2 factors are sufficient.
The chi square statistic is 91.57 on 43 degrees of freedom.
The p-value is 2.3e-05
La varianza de SL5, SL6, SL9, SL8, SL7, SL1, SL10, SL11 y SL12 estan contenidas dentro del primer factor
La varianza de SL2, SL3, SL4 estan contenidas dentro del segundo factor.
Se observa que no es necesaria la eliminación de items para resumir la varianza en nuevas variables. El analisis factorial ya es suficientemente bueno, explicando una varianza acumulada del 71%.
Visualizemos las cargas para observar mejor el patron de captura de la varianza total por cada factor.
En el caso de Satisfacción Laboral se observa un patron claro de división entre dos factores. El Factor 1 representa mayoritariamente la Satisfacción por Supervisión y por Prestaciones. Por otro lado el Factor 2 refiere mayoritariamente a la Satisfacción por el Ambiente Físico.
Ahora se pueden generar nuevas variables calculando los “scores” en Satisfacción Laboral para cada una de las 50 observaciones.
$`Satisfacción Laboral`
Factor1 Factor2
[1,] 0.59703362 2.01110040
[2,] 0.30951283 -0.88260586
[3,] 0.71753910 -0.23483281
[4,] 1.32414698 1.12908007
[5,] 1.05696922 -0.29504847
[6,] -0.03513190 -0.07636506
[7,] 0.43619263 -0.92911476
[8,] 1.00072180 0.46577204
[9,] 1.13125094 0.42970312
[10,] -1.32329795 0.92008867
[11,] 0.70371017 -0.99717042
[12,] 1.14999504 1.16706462
[13,] -1.59889201 0.23787936
[14,] 1.20827007 -0.33719540
[15,] -2.05356050 -1.16579027
[16,] -0.83331208 0.83586262
[17,] 0.35972457 0.58715143
[18,] -1.29016100 0.17188625
[19,] -0.71387926 0.80056790
[20,] 0.14698583 0.62765896
[21,] 0.56609520 1.29276190
[22,] -0.71387926 0.80056790
[23,] -0.30115661 0.70497682
[24,] 0.47864432 1.30307714
[25,] 0.03293525 0.64736866
[26,] 0.59730070 -0.20650871
[27,] 0.87429518 -2.51746841
[28,] 2.17689367 -1.27009211
[29,] 0.86273118 0.48951735
[30,] 1.66353519 -1.92124958
[31,] -0.79028256 0.07937243
[32,] -0.27257521 -0.03261298
[33,] -0.16752338 -1.55413143
[34,] 1.28931254 0.39526030
[35,] -1.14610579 -0.60578700
[36,] -0.94536996 0.11196951
[37,] -0.47323144 0.76034803
[38,] -0.87798478 0.83515629
[39,] 0.12292860 0.63776463
[40,] -1.30251192 -2.07197931
[41,] 1.30114347 -0.36196236
[42,] 0.72926441 1.23590786
[43,] -1.21657004 -0.58867062
[44,] -0.54753190 -0.72010317
[45,] -1.13619866 -1.34491998
[46,] -0.49736160 -0.73512736
[47,] -0.18658398 -1.53170027
[48,] -1.03604029 0.11968699
[49,] -1.04693684 0.85675304
[50,] -0.33105358 0.72613209
Rondas.de.eliminacion | Statistic | Valor_p | Numero_Factores | Numero.obs | Grados.de.Libertad | Numero.items.incluidos | KMO | Varianza.Acumulada | |
---|---|---|---|---|---|---|---|---|---|
objective | 1 | 91.56549 | 2.3e-05 | 2 | 50 | 43 | 12 | 0.8576093 | 0.7056515 |
Para el proceso realizado con el workEngagement
Global
Reliability analysis
Call: alpha(x = WorkEngagement)
raw_alpha std.alpha G6(smc) average_r S/N ase mean sd
0.92 0.92 0.96 0.41 12 0.016 4.4 0.75
lower alpha upper 95% confidence boundaries
0.89 0.92 0.95
Reliability if an item is dropped:
raw_alpha std.alpha G6(smc) average_r S/N alpha se NA
UVWES1 0.91 0.91 0.95 0.40 11 0.018 0.022
UVWES2 0.92 0.92 0.96 0.42 12 0.017 0.025
UVWES3 0.91 0.92 0.95 0.41 11 0.018 0.024
UVWES4 0.91 0.91 0.95 0.40 11 0.018 0.023
UVWES5 0.92 0.92 0.96 0.42 12 0.017 0.023
UVWES6 0.92 0.92 0.96 0.43 12 0.016 0.023
UVWES7 0.92 0.92 0.96 0.42 11 0.017 0.024
UVWES8 0.92 0.92 0.96 0.42 12 0.017 0.025
UVWES9 0.92 0.92 0.96 0.41 11 0.017 0.024
UVWES10 0.91 0.92 0.95 0.40 11 0.018 0.023
UVWES11 0.91 0.91 0.95 0.40 11 0.018 0.023
UVWES12 0.91 0.92 0.96 0.41 11 0.018 0.023
UVWES13 0.91 0.91 0.95 0.40 11 0.018 0.023
UVWES14 0.91 0.92 0.96 0.41 11 0.018 0.024
UVWES15 0.91 0.92 0.95 0.41 11 0.018 0.023
UVWES16 0.92 0.93 0.96 0.44 12 0.016 0.020
UVWES17 0.92 0.92 0.96 0.42 11 0.017 0.025
Item statistics
n raw.r std.r r.cor r.drop mean sd
UVWES1 50 0.80 0.80 0.80 0.76 4.3 1.12
UVWES2 50 0.60 0.60 0.58 0.54 4.6 1.03
UVWES3 50 0.70 0.70 0.69 0.65 4.4 1.26
UVWES4 50 0.78 0.79 0.78 0.75 4.5 0.99
UVWES5 50 0.55 0.56 0.54 0.49 4.6 0.97
UVWES6 50 0.52 0.52 0.48 0.45 4.1 1.22
UVWES7 50 0.63 0.64 0.63 0.59 4.6 0.93
UVWES8 50 0.60 0.61 0.58 0.55 4.3 1.05
UVWES9 50 0.66 0.66 0.65 0.61 4.3 1.14
UVWES10 50 0.74 0.75 0.75 0.70 4.8 1.08
UVWES11 50 0.79 0.79 0.79 0.75 4.4 0.95
UVWES12 50 0.70 0.70 0.69 0.65 4.3 1.21
UVWES13 50 0.79 0.79 0.79 0.75 4.3 1.22
UVWES14 50 0.69 0.69 0.68 0.63 4.3 1.12
UVWES15 50 0.75 0.74 0.74 0.70 4.5 1.20
UVWES16 50 0.42 0.41 0.38 0.33 4.0 1.32
UVWES17 50 0.63 0.62 0.59 0.57 4.2 1.20
Non missing response frequency for each item
0 1 2 3 4 5 6 miss
UVWES1 0.00 0.00 0.06 0.22 0.24 0.36 0.12 0
UVWES2 0.00 0.00 0.04 0.10 0.22 0.46 0.18 0
UVWES3 0.00 0.00 0.10 0.14 0.26 0.28 0.22 0
UVWES4 0.00 0.00 0.02 0.18 0.22 0.46 0.12 0
UVWES5 0.00 0.00 0.02 0.12 0.30 0.40 0.16 0
UVWES6 0.02 0.02 0.06 0.14 0.36 0.34 0.06 0
UVWES7 0.00 0.00 0.02 0.10 0.32 0.42 0.14 0
UVWES8 0.00 0.00 0.06 0.16 0.30 0.38 0.10 0
UVWES9 0.00 0.00 0.06 0.22 0.26 0.32 0.14 0
UVWES10 0.00 0.00 0.02 0.12 0.24 0.32 0.30 0
UVWES11 0.00 0.00 0.02 0.14 0.36 0.36 0.12 0
UVWES12 0.02 0.00 0.04 0.16 0.32 0.32 0.14 0
UVWES13 0.00 0.02 0.04 0.20 0.24 0.32 0.18 0
UVWES14 0.00 0.00 0.06 0.18 0.36 0.24 0.16 0
UVWES15 0.02 0.00 0.04 0.04 0.38 0.30 0.22 0
UVWES16 0.02 0.04 0.06 0.14 0.34 0.32 0.08 0
UVWES17 0.00 0.02 0.04 0.20 0.34 0.22 0.18 0
Luego de la primera eliminacion de variables
Reliability analysis
Call: alpha(x = WorkEngagement1)
raw_alpha std.alpha G6(smc) average_r S/N ase mean sd
0.88 0.88 0.92 0.36 7.3 0.026 4.4 0.72
lower alpha upper 95% confidence boundaries
0.83 0.88 0.93
Reliability if an item is dropped:
raw_alpha std.alpha G6(smc) average_r S/N alpha se NA
UVWES2 0.87 0.87 0.91 0.36 6.8 0.028 0.020
UVWES3 0.86 0.87 0.90 0.35 6.5 0.029 0.018
UVWES4 0.86 0.86 0.90 0.34 6.3 0.029 0.017
UVWES5 0.87 0.88 0.92 0.37 7.1 0.027 0.017
UVWES6 0.87 0.88 0.92 0.37 7.1 0.026 0.018
UVWES7 0.87 0.87 0.91 0.36 6.7 0.028 0.019
UVWES8 0.87 0.87 0.91 0.36 6.7 0.028 0.021
UVWES9 0.87 0.87 0.91 0.36 6.6 0.028 0.019
UVWES12 0.86 0.87 0.91 0.36 6.6 0.028 0.019
UVWES14 0.87 0.87 0.91 0.36 6.6 0.028 0.019
UVWES15 0.86 0.86 0.90 0.35 6.4 0.029 0.018
UVWES16 0.88 0.88 0.92 0.38 7.3 0.025 0.018
UVWES17 0.87 0.87 0.92 0.36 6.7 0.028 0.021
Item statistics
n raw.r std.r r.cor r.drop mean sd
UVWES2 50 0.62 0.63 0.60 0.54 4.6 1.03
UVWES3 50 0.70 0.69 0.69 0.62 4.4 1.26
UVWES4 50 0.77 0.77 0.77 0.72 4.5 0.99
UVWES5 50 0.53 0.54 0.50 0.44 4.6 0.97
UVWES6 50 0.54 0.53 0.48 0.44 4.1 1.22
UVWES7 50 0.63 0.64 0.63 0.57 4.6 0.93
UVWES8 50 0.64 0.64 0.62 0.56 4.3 1.05
UVWES9 50 0.66 0.67 0.65 0.58 4.3 1.14
UVWES12 50 0.68 0.67 0.65 0.60 4.3 1.21
UVWES14 50 0.66 0.66 0.64 0.58 4.3 1.12
UVWES15 50 0.74 0.73 0.73 0.67 4.5 1.20
UVWES16 50 0.49 0.48 0.42 0.37 4.0 1.32
UVWES17 50 0.66 0.64 0.60 0.57 4.2 1.20
Non missing response frequency for each item
0 1 2 3 4 5 6 miss
UVWES2 0.00 0.00 0.04 0.10 0.22 0.46 0.18 0
UVWES3 0.00 0.00 0.10 0.14 0.26 0.28 0.22 0
UVWES4 0.00 0.00 0.02 0.18 0.22 0.46 0.12 0
UVWES5 0.00 0.00 0.02 0.12 0.30 0.40 0.16 0
UVWES6 0.02 0.02 0.06 0.14 0.36 0.34 0.06 0
UVWES7 0.00 0.00 0.02 0.10 0.32 0.42 0.14 0
UVWES8 0.00 0.00 0.06 0.16 0.30 0.38 0.10 0
UVWES9 0.00 0.00 0.06 0.22 0.26 0.32 0.14 0
UVWES12 0.02 0.00 0.04 0.16 0.32 0.32 0.14 0
UVWES14 0.00 0.00 0.06 0.18 0.36 0.24 0.16 0
UVWES15 0.02 0.00 0.04 0.04 0.38 0.30 0.22 0
UVWES16 0.02 0.04 0.06 0.14 0.34 0.32 0.08 0
UVWES17 0.00 0.02 0.04 0.20 0.34 0.22 0.18 0
luego de la segunda eliminación de variables
Reliability analysis
Call: alpha(x = WorkEngagement2)
raw_alpha std.alpha G6(smc) average_r S/N ase mean sd
0.85 0.85 0.89 0.39 5.8 0.032 4.4 0.76
lower alpha upper 95% confidence boundaries
0.79 0.85 0.91
Reliability if an item is dropped:
raw_alpha std.alpha G6(smc) average_r S/N alpha se NA
UVWES3 0.83 0.83 0.87 0.38 5.0 0.037 0.024
UVWES4 0.82 0.82 0.85 0.36 4.6 0.038 0.023
UVWES5 0.85 0.85 0.88 0.41 5.6 0.033 0.023
UVWES6 0.85 0.85 0.89 0.42 5.7 0.032 0.022
UVWES7 0.84 0.84 0.88 0.40 5.4 0.034 0.024
UVWES9 0.84 0.84 0.88 0.40 5.3 0.034 0.026
UVWES12 0.83 0.84 0.87 0.39 5.1 0.036 0.025
UVWES14 0.84 0.84 0.87 0.39 5.1 0.035 0.026
UVWES15 0.82 0.83 0.86 0.37 4.8 0.038 0.023
Item statistics
n raw.r std.r r.cor r.drop mean sd
UVWES3 50 0.73 0.72 0.70 0.62 4.4 1.26
UVWES4 50 0.80 0.81 0.81 0.74 4.5 0.99
UVWES5 50 0.57 0.59 0.53 0.47 4.6 0.97
UVWES6 50 0.58 0.56 0.49 0.44 4.1 1.22
UVWES7 50 0.61 0.62 0.58 0.52 4.6 0.93
UVWES9 50 0.66 0.66 0.61 0.54 4.3 1.14
UVWES12 50 0.71 0.70 0.66 0.60 4.3 1.21
UVWES14 50 0.67 0.68 0.64 0.57 4.3 1.12
UVWES15 50 0.77 0.76 0.75 0.68 4.5 1.20
Non missing response frequency for each item
0 1 2 3 4 5 6 miss
UVWES3 0.00 0.00 0.10 0.14 0.26 0.28 0.22 0
UVWES4 0.00 0.00 0.02 0.18 0.22 0.46 0.12 0
UVWES5 0.00 0.00 0.02 0.12 0.30 0.40 0.16 0
UVWES6 0.02 0.02 0.06 0.14 0.36 0.34 0.06 0
UVWES7 0.00 0.00 0.02 0.10 0.32 0.42 0.14 0
UVWES9 0.00 0.00 0.06 0.22 0.26 0.32 0.14 0
UVWES12 0.02 0.00 0.04 0.16 0.32 0.32 0.14 0
UVWES14 0.00 0.00 0.06 0.18 0.36 0.24 0.16 0
UVWES15 0.02 0.00 0.04 0.04 0.38 0.30 0.22 0
Ahora para el proceso realizado con la satisfacción Laboral
Reliability analysis
Call: alpha(x = SatisfacciónLaboral)
raw_alpha std.alpha G6(smc) average_r S/N ase mean sd
0.93 0.93 0.97 0.53 14 0.015 4.5 1
lower alpha upper 95% confidence boundaries
0.9 0.93 0.96
Reliability if an item is dropped:
raw_alpha std.alpha G6(smc) average_r S/N alpha se NA
SL1 0.92 0.93 0.96 0.53 12 0.017 0.053
SL2 0.94 0.94 0.96 0.58 15 0.014 0.041
SL3 0.93 0.93 0.96 0.55 14 0.015 0.051
SL4 0.94 0.94 0.97 0.58 15 0.014 0.044
SL5 0.92 0.92 0.96 0.52 12 0.017 0.048
SL6 0.92 0.92 0.96 0.52 12 0.018 0.049
SL7 0.92 0.92 0.96 0.51 11 0.018 0.050
SL8 0.92 0.92 0.96 0.52 12 0.018 0.051
SL9 0.92 0.92 0.96 0.52 12 0.017 0.049
SL10 0.92 0.92 0.96 0.52 12 0.017 0.049
SL11 0.92 0.92 0.96 0.52 12 0.017 0.047
SL12 0.92 0.93 0.96 0.54 13 0.016 0.051
Item statistics
n raw.r std.r r.cor r.drop mean sd
SL1 50 0.78 0.78 0.76 0.73 5.0 1.2
SL2 50 0.50 0.49 0.47 0.40 4.3 1.4
SL3 50 0.64 0.63 0.62 0.56 4.1 1.4
SL4 50 0.51 0.50 0.45 0.41 4.1 1.4
SL5 50 0.83 0.83 0.82 0.79 4.8 1.4
SL6 50 0.86 0.86 0.86 0.83 4.7 1.5
SL7 50 0.90 0.91 0.91 0.88 4.6 1.3
SL8 50 0.86 0.86 0.86 0.83 4.5 1.2
SL9 50 0.82 0.82 0.81 0.78 4.5 1.3
SL10 50 0.83 0.84 0.83 0.79 4.8 1.4
SL11 50 0.81 0.82 0.81 0.77 4.6 1.2
SL12 50 0.73 0.74 0.72 0.68 4.4 1.2
Non missing response frequency for each item
1 2 3 4 5 6 7 miss
SL1 0.00 0.02 0.10 0.16 0.38 0.24 0.10 0
SL2 0.08 0.06 0.06 0.28 0.38 0.12 0.02 0
SL3 0.04 0.10 0.16 0.24 0.34 0.10 0.02 0
SL4 0.04 0.12 0.16 0.20 0.32 0.14 0.02 0
SL5 0.00 0.08 0.06 0.30 0.18 0.26 0.12 0
SL6 0.00 0.08 0.06 0.40 0.14 0.16 0.16 0
SL7 0.00 0.06 0.12 0.32 0.24 0.20 0.06 0
SL8 0.00 0.06 0.10 0.40 0.18 0.22 0.04 0
SL9 0.00 0.06 0.18 0.28 0.24 0.20 0.04 0
SL10 0.00 0.02 0.16 0.28 0.20 0.18 0.16 0
SL11 0.00 0.04 0.16 0.28 0.32 0.12 0.08 0
SL12 0.02 0.02 0.16 0.32 0.30 0.14 0.04 0
Ahora se pueden usar las puntuaciones obtenidas con el analisis factorial para buscar relaciones entre la satisfacción y el work engagement.
Examinemos visualmente las relaciones, para estimar candidatos para posteriores regresiones lineakes
Parece que si existen relaciones entre las dimensiones del WorkEngagenet y la Satisfacción Laboral. Examinemos estas mas a fondo.
Empezemos con relacionar los puntajes del Factor 1 de la Satisfacción Laboral (como variable independiente) con los puntajes de ambos factores de Work Engagement (Variable Dependiente)
Podemos observar una clara relación positiva del Factor1 de la Satisfacción Laboral con el Factor 1 del Work Engagement. La relación con el Factor 2 no es estadisticamente significativa.
Examinemos las tablas de coeficientes de regresión
Para el primer caso: (WE1 vs SL1)
Call:
lm(formula = newDatTotal$WorkEngagement_Factor1 ~ newDatTotal$SatisfacciónLaboral_Factor1)
Residuals:
Min 1Q Median 3Q Max
-1.9447 -0.5471 0.1072 0.4340 1.8045
Coefficients:
Estimate Std. Error t value
(Intercept) -1.557e-16 1.134e-01 0.000
newDatTotal$SatisfacciónLaboral_Factor1 4.274e-01 1.172e-01 3.646
Pr(>|t|)
(Intercept) 1.000000
newDatTotal$SatisfacciónLaboral_Factor1 0.000654 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 0.8021 on 48 degrees of freedom
Multiple R-squared: 0.2169, Adjusted R-squared: 0.2006
F-statistic: 13.29 on 1 and 48 DF, p-value: 0.000654
La tabla nos muestra la significancia estadistica de la regresión (p menor a 0.05). Tambien podemos obtener el R cuadrado. Que refiere a la fuerza de asociación entre ambas variables. En este caso el modelo explica el 21.94% de la variación del Factor 1 de WorkEngagement en relacion al factor 1 de la Satisfacción Laboral (Que hacia referencia a satisfacción con el ambiente fisico). Esta relacion nos indica que existe una relacion estadisticamente significativa entre una mayor satisfacción con el ambiente fisico y un incremento en el Work Engagement especificamente en los items UVWES5, UVWES6 y UVWES15.
Examinemos la tabla para la segunda relación
Call:
lm(formula = newDatTotal$WorkEngagement_Factor2 ~ newDatTotal$SatisfacciónLaboral_Factor1)
Residuals:
Min 1Q Median 3Q Max
-4.0484 -0.3254 0.0910 0.5596 1.3078
Coefficients:
Estimate Std. Error t value
(Intercept) -9.279e-18 1.348e-01 0.00
newDatTotal$SatisfacciónLaboral_Factor1 7.387e-02 1.393e-01 0.53
Pr(>|t|)
(Intercept) 1.000
newDatTotal$SatisfacciónLaboral_Factor1 0.598
Residual standard error: 0.9532 on 48 degrees of freedom
Multiple R-squared: 0.005824, Adjusted R-squared: -0.01489
F-statistic: 0.2812 on 1 and 48 DF, p-value: 0.5984
Como se puede observar por la tabla, NO existe una relación significativa (p = 0.6017) entre el Factor 2 de Work Engagement y el Factor 1 de Satisfacción Laboral. Esto nos indica que no existe relacion alguna entre el Factor 1 de Satisfacción Laboral (i.e. Mayormente Satisfacción con el Ambiente Fisico) y el Factor 2 del Work Engagement (UVWES4, UVWES9, UVWES12, UVWES14, UVWES7).
Enfocandonos en la primera relación significativa. Se puede desglosar mas las relaciones por variables sociodemográficas. Por ejemplo desglosando la relación entre sexo
Ahora observamos un patron bastante interesante al desglosar la relación anterior entre hombres y mujeres. Al parecer el patron es unicamente dirigido por las mujeres. El patron deja de ser significativo para los hombres. Observemos las tablas con los coeficientes.
Hombres:
Call:
lm(formula = newDatTotal$WorkEngagement_Factor1[newDatTotal$sexo ==
"M"] ~ newDatTotal$SatisfacciónLaboral_Factor1[newDatTotal$sexo ==
"M"])
Residuals:
Min 1Q Median 3Q Max
-2.22384 -0.50884 0.03682 0.55584 1.50610
Coefficients:
Estimate
(Intercept) 0.06004
newDatTotal$SatisfacciónLaboral_Factor1[newDatTotal$sexo == "M"] 0.24728
Std. Error
(Intercept) 0.15411
newDatTotal$SatisfacciónLaboral_Factor1[newDatTotal$sexo == "M"] 0.16205
t value
(Intercept) 0.390
newDatTotal$SatisfacciónLaboral_Factor1[newDatTotal$sexo == "M"] 1.526
Pr(>|t|)
(Intercept) 0.700
newDatTotal$SatisfacciónLaboral_Factor1[newDatTotal$sexo == "M"] 0.137
Residual standard error: 0.8716 on 30 degrees of freedom
Multiple R-squared: 0.07203, Adjusted R-squared: 0.0411
F-statistic: 2.329 on 1 and 30 DF, p-value: 0.1375
Mujeres:
Call:
lm(formula = newDatTotal$WorkEngagement_Factor1[newDatTotal$sexo ==
"F"] ~ newDatTotal$SatisfacciónLaboral_Factor1[newDatTotal$sexo ==
"F"])
Residuals:
Min 1Q Median 3Q Max
-0.83153 -0.32572 -0.08993 0.28227 1.19710
Coefficients:
Estimate
(Intercept) -0.1241
newDatTotal$SatisfacciónLaboral_Factor1[newDatTotal$sexo == "F"] 0.7258
Std. Error
(Intercept) 0.1345
newDatTotal$SatisfacciónLaboral_Factor1[newDatTotal$sexo == "F"] 0.1349
t value
(Intercept) -0.923
newDatTotal$SatisfacciónLaboral_Factor1[newDatTotal$sexo == "F"] 5.379
Pr(>|t|)
(Intercept) 0.37
newDatTotal$SatisfacciónLaboral_Factor1[newDatTotal$sexo == "F"] 6.15e-05
(Intercept)
newDatTotal$SatisfacciónLaboral_Factor1[newDatTotal$sexo == "F"] ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 0.5701 on 16 degrees of freedom
Multiple R-squared: 0.6439, Adjusted R-squared: 0.6217
F-statistic: 28.93 on 1 and 16 DF, p-value: 6.146e-05
Ahora examinemos las relaciones de los scores del Work Engagement con el los Scores del Factor 2 de la Satisfacción Laboral.
El factor 2 de la Satisfacción Laboral no presenta relaciones estadisticamente signifactivas con ningun de los factores del Work Engagement.
Examinemos las tablas mas a fondo
Factor 2 SL vs Factor 1 WE
Call:
lm(formula = newDatTotal$WorkEngagement_Factor1 ~ newDatTotal$SatisfacciónLaboral_Factor2)
Residuals:
Min 1Q Median 3Q Max
-2.37171 -0.48721 0.07159 0.53337 1.75450
Coefficients:
Estimate Std. Error t value
(Intercept) -5.249e-17 1.262e-01 0.000
newDatTotal$SatisfacciónLaboral_Factor2 1.579e-01 1.280e-01 1.234
Pr(>|t|)
(Intercept) 1.000
newDatTotal$SatisfacciónLaboral_Factor2 0.223
Residual standard error: 0.8923 on 48 degrees of freedom
Multiple R-squared: 0.03073, Adjusted R-squared: 0.01054
F-statistic: 1.522 on 1 and 48 DF, p-value: 0.2233
Como podemos observar, el p es muy cerca a 0.05. Lo que nos sugiere la presencia de algun patron en la regresión. Desglosemos esta relación en particular por sexo como habiamos hecho anteriormente para la el Factor 1 de Satisfacción Laboral.
No parece existir relaciones significativas. Examinemos las tablas
Hombres
Call:
lm(formula = newDatTotal$WorkEngagement_Factor1[newDatTotal$sexo ==
"M"] ~ newDatTotal$SatisfacciónLaboral_Factor2[newDatTotal$sexo ==
"M"])
Residuals:
Min 1Q Median 3Q Max
-2.46674 -0.34891 -0.01983 0.51985 1.51344
Coefficients:
Estimate
(Intercept) 0.05045
newDatTotal$SatisfacciónLaboral_Factor2[newDatTotal$sexo == "M"] 0.08214
Std. Error
(Intercept) 0.15972
newDatTotal$SatisfacciónLaboral_Factor2[newDatTotal$sexo == "M"] 0.18174
t value
(Intercept) 0.316
newDatTotal$SatisfacciónLaboral_Factor2[newDatTotal$sexo == "M"] 0.452
Pr(>|t|)
(Intercept) 0.754
newDatTotal$SatisfacciónLaboral_Factor2[newDatTotal$sexo == "M"] 0.655
Residual standard error: 0.9017 on 30 degrees of freedom
Multiple R-squared: 0.006762, Adjusted R-squared: -0.02635
F-statistic: 0.2042 on 1 and 30 DF, p-value: 0.6546
Mujeres
Call:
lm(formula = newDatTotal$WorkEngagement_Factor1[newDatTotal$sexo ==
"F"] ~ newDatTotal$SatisfacciónLaboral_Factor2[newDatTotal$sexo ==
"F"])
Residuals:
Min 1Q Median 3Q Max
-1.4717 -0.6097 0.1238 0.4341 1.6758
Coefficients:
Estimate
(Intercept) -0.07546
newDatTotal$SatisfacciónLaboral_Factor2[newDatTotal$sexo == "F"] 0.22676
Std. Error
(Intercept) 0.21634
newDatTotal$SatisfacciónLaboral_Factor2[newDatTotal$sexo == "F"] 0.18769
t value
(Intercept) -0.349
newDatTotal$SatisfacciónLaboral_Factor2[newDatTotal$sexo == "F"] 1.208
Pr(>|t|)
(Intercept) 0.732
newDatTotal$SatisfacciónLaboral_Factor2[newDatTotal$sexo == "F"] 0.245
Residual standard error: 0.9145 on 16 degrees of freedom
Multiple R-squared: 0.08361, Adjusted R-squared: 0.02633
F-statistic: 1.46 on 1 and 16 DF, p-value: 0.2445
La significancia de la relación es incluso mejor separando por sexos. Tal ves existe otra variable sociodemografica que explica la relación entre estos dos factores. Continuemos con la examinación
No existen relaciones significativas.
Factor 2 SL vs Factor 2 WE
Call:
lm(formula = newDatTotal$WorkEngagement_Factor2 ~ newDatTotal$SatisfacciónLaboral_Factor2)
Residuals:
Min 1Q Median 3Q Max
-3.9140 -0.3754 0.0375 0.4891 1.3200
Coefficients:
Estimate Std. Error t value
(Intercept) 3.321e-17 1.344e-01 0.000
newDatTotal$SatisfacciónLaboral_Factor2 1.058e-01 1.362e-01 0.776
Pr(>|t|)
(Intercept) 1.000
newDatTotal$SatisfacciónLaboral_Factor2 0.441
Residual standard error: 0.95 on 48 degrees of freedom
Multiple R-squared: 0.0124, Adjusted R-squared: -0.008176
F-statistic: 0.6026 on 1 and 48 DF, p-value: 0.4414
En este caso, no observamos relaciones estadisticamente significativas.
Visualizando las correlaciones
Podemos confirmar con las correlaciones la relacion positiva existente entre el factor 1 de la Satisfacción Laboral con el Factor 1 del Work Engagement.
Tabla con valores de las correlaciones:
WorkEngagement_Factor1 | WorkEngagement_Factor2 | SatisfacciónLaboral_Factor1 | SatisfacciónLaboral_Factor2 | |
---|---|---|---|---|
WorkEngagement_Factor1 | 1.0000000 | 0.0885842 | 0.4657098 | 0.1753022 |
WorkEngagement_Factor2 | 0.0885842 | 1.0000000 | 0.0763159 | 0.1113515 |
SatisfacciónLaboral_Factor1 | 0.4657098 | 0.0763159 | 1.0000000 | 0.0107370 |
SatisfacciónLaboral_Factor2 | 0.1753022 | 0.1113515 | 0.0107370 | 1.0000000 |
Examinemos los estadisticos de las correlaciones “Pearson’s product moment correlation”
Correlaciones | Estadistico.Pearson.s_product.moment_correlation | Valor.p | Grados.de.Libertad |
---|---|---|---|
WorkEngagement_Factor1-SatisfacciónLaboral_Factor1 | 3.6460560 | 0.0006540 | 48 |
WorkEngagement_Factor2-SatisfacciónLaboral_Factor1 | 1.2336328 | 0.2233465 | 48 |
WorkEngagement_Factor1-SatisfacciónLaboral_Factor2 | 0.5302784 | 0.5983636 | 48 |
WorkEngagement_Factor2-SatisfacciónLaboral_Factor2 | 0.7762932 | 0.4413844 | 48 |
Basados en los valores de p podemos afirmar que la unica correlacion significativa es la existente entre el Factor 1 de la Satisfacción Laboral con el Factor 1 del Work Engagement.
Tablas y graficos sumarizando la información demográfica
rank | edad | sexo | nombramiento | tiempoServicio | |
---|---|---|---|---|---|
Min. : 1.00 | 25-35:11 | F:18 | Definitivo :31 | 1-10 :30 | |
1st Qu.:13.25 | 36-40:11 | M:32 | Provisional:19 | 11-20:13 | |
Median :25.50 | 41-45: 5 | 21-35: 7 | |||
Mean :25.50 | 46-50:11 | ||||
3rd Qu.:37.75 | 51-55: 8 | ||||
Max. :50.00 | 56-60: 4 |
La relación entre variables es analizada para cada combinación de preguntas entre dimensiones de Work Engagement y Satisfacción laboral. Relaciones entre variables son exploradas por medio de correlaciónes y regresiones lineares.
La Correlación es una técnica estadística usada para determinar la relación entre dos o más variables. La relación entre la duración de una carrera de distancia y el test del escalón, o la relación entre las características de la personalidad y la participación en deportes de alto riesgo. La correlación puede ser de al menos dos variables o de una variable dependiente y dos o más variables independientes, denominada correlación múltiple.
El Coeficiente de Correlación es un valor cuantitativo de la relación entre dos o más variables. La coeficiente de correlación puede variar desde -1.00 hasta 1.00. La correlación de proporcionalidad directa o positiva se establece con los valores +1.00 y de proporcionalidad inversa o negativa, con -1.00. No existe relación entre las variables cuando el coeficiente es de 0.00.
Si utilizamos un sistema de coordenadas cartesianas para representar la distribución bidimensional, obtendremos un conjunto de puntos conocido con el diagrama de dispersión, cuyo análisis permite estudiar cualitativamente, la relación entre ambas variables tal como se ve en la figura. El siguiente paso, es la determinación de la dependencia funcional entre las dos variables x e y que mejor ajusta a la distribución bidimensional. Se denomina regresión lineal cuando la función es lineal, es decir, requiere la determinación de dos parámetros: la pendiente y la ordenada en el origen de la recta de regresión, y=ax+b. La regresión nos permite además, determinar el grado de dependencia de las series de valores X e Y, prediciendo el valor y estimado que se obtendría para un valor x que no esté en la distribución. Para las regresiones lineales lineas sólidas indican valores estadisticos significantes (p < 0.05)
UVWES1 | UVWES2 | UVWES3 | UVWES4 | UVWES5 | UVWES6 | UVWES7 | |
---|---|---|---|---|---|---|---|
UVWES1 | 1 | 0.4735 | 0.6653 | 0.636 | 0.4627 | 0.5407 | 0.5428 |
UVWES2 | 0.4735 | 1 | 0.503 | 0.3129 | 0.1859 | 0.2789 | 0.5585 |
UVWES3 | 0.6653 | 0.503 | 1 | 0.6983 | 0.3225 | 0.4366 | 0.4246 |
UVWES4 | 0.636 | 0.3129 | 0.6983 | 1 | 0.5816 | 0.2787 | 0.3435 |
UVWES5 | 0.4627 | 0.1859 | 0.3225 | 0.5816 | 1 | 0.126 | 0.1653 |
UVWES6 | 0.5407 | 0.2789 | 0.4366 | 0.2787 | 0.126 | 1 | 0.4021 |
UVWES7 | 0.5428 | 0.5585 | 0.4246 | 0.3435 | 0.1653 | 0.4021 | 1 |
UVWES8 | 0.4676 | 0.2718 | 0.3118 | 0.4047 | 0.41 | 0.3032 | 0.3665 |
UVWES9 | 0.4731 | 0.3437 | 0.2141 | 0.4098 | 0.4554 | 0.2089 | 0.303 |
UVWES10 | 0.592 | 0.3443 | 0.5635 | 0.6605 | 0.4806 | 0.2748 | 0.5028 |
UVWES11 | 0.6812 | 0.4309 | 0.5121 | 0.5817 | 0.3811 | 0.3833 | 0.4218 |
UVWES12 | 0.5156 | 0.2632 | 0.4365 | 0.5461 | 0.4354 | 0.2507 | 0.1296 |
UVWES13 | 0.5148 | 0.409 | 0.4577 | 0.6519 | 0.5405 | 0.2462 | 0.4577 |
UVWES14 | 0.5131 | 0.4913 | 0.2609 | 0.4896 | 0.3504 | 0.1376 | 0.4253 |
UVWES15 | 0.6676 | 0.3938 | 0.6045 | 0.5826 | 0.173 | 0.5779 | 0.6206 |
UVWES16 | 0.03786 | 0.2473 | 0.1675 | 0.273 | 0.08671 | 0.1899 | 0.3742 |
UVWES17 | 0.3607 | 0.3522 | 0.3824 | 0.4809 | 0.214 | 0.2262 | 0.2421 |
UVWES8 | UVWES9 | UVWES10 | UVWES11 | UVWES12 | UVWES13 | |
---|---|---|---|---|---|---|
UVWES1 | 0.4676 | 0.4731 | 0.592 | 0.6812 | 0.5156 | 0.5148 |
UVWES2 | 0.2718 | 0.3437 | 0.3443 | 0.4309 | 0.2632 | 0.409 |
UVWES3 | 0.3118 | 0.2141 | 0.5635 | 0.5121 | 0.4365 | 0.4577 |
UVWES4 | 0.4047 | 0.4098 | 0.6605 | 0.5817 | 0.5461 | 0.6519 |
UVWES5 | 0.41 | 0.4554 | 0.4806 | 0.3811 | 0.4354 | 0.5405 |
UVWES6 | 0.3032 | 0.2089 | 0.2748 | 0.3833 | 0.2507 | 0.2462 |
UVWES7 | 0.3665 | 0.303 | 0.5028 | 0.4218 | 0.1296 | 0.4577 |
UVWES8 | 1 | 0.6131 | 0.4588 | 0.2996 | 0.3 | 0.2992 |
UVWES9 | 0.6131 | 1 | 0.4665 | 0.5195 | 0.5517 | 0.5506 |
UVWES10 | 0.4588 | 0.4665 | 1 | 0.5781 | 0.4264 | 0.5734 |
UVWES11 | 0.2996 | 0.5195 | 0.5781 | 1 | 0.7641 | 0.5602 |
UVWES12 | 0.3 | 0.5517 | 0.4264 | 0.7641 | 1 | 0.6365 |
UVWES13 | 0.2992 | 0.5506 | 0.5734 | 0.5602 | 0.6365 | 1 |
UVWES14 | 0.2606 | 0.5529 | 0.5077 | 0.5853 | 0.5456 | 0.7232 |
UVWES15 | 0.4342 | 0.3284 | 0.6856 | 0.478 | 0.3571 | 0.5545 |
UVWES16 | 0.2895 | 0.2005 | 0.0465 | 0.238 | 0.2775 | 0.3633 |
UVWES17 | 0.3919 | 0.355 | 0.3904 | 0.5523 | 0.4838 | 0.4008 |
UVWES14 | UVWES15 | UVWES16 | UVWES17 | |
---|---|---|---|---|
UVWES1 | 0.5131 | 0.6676 | 0.03786 | 0.3607 |
UVWES2 | 0.4913 | 0.3938 | 0.2473 | 0.3522 |
UVWES3 | 0.2609 | 0.6045 | 0.1675 | 0.3824 |
UVWES4 | 0.4896 | 0.5826 | 0.273 | 0.4809 |
UVWES5 | 0.3504 | 0.173 | 0.08671 | 0.214 |
UVWES6 | 0.1376 | 0.5779 | 0.1899 | 0.2262 |
UVWES7 | 0.4253 | 0.6206 | 0.3742 | 0.2421 |
UVWES8 | 0.2606 | 0.4342 | 0.2895 | 0.3919 |
UVWES9 | 0.5529 | 0.3284 | 0.2005 | 0.355 |
UVWES10 | 0.5077 | 0.6856 | 0.0465 | 0.3904 |
UVWES11 | 0.5853 | 0.478 | 0.238 | 0.5523 |
UVWES12 | 0.5456 | 0.3571 | 0.2775 | 0.4838 |
UVWES13 | 0.7232 | 0.5545 | 0.3633 | 0.4008 |
UVWES14 | 1 | 0.3944 | 0.2037 | 0.3909 |
UVWES15 | 0.3944 | 1 | 0.2128 | 0.403 |
UVWES16 | 0.2037 | 0.2128 | 1 | 0.4343 |
UVWES17 | 0.3909 | 0.403 | 0.4343 | 1 |
SL1 | SL2 | SL3 | SL4 | SL5 | SL6 | SL7 | |
---|---|---|---|---|---|---|---|
SL1 | 1 | 0.3708 | 0.2883 | 0.2367 | 0.7048 | 0.7114 | 0.6511 |
SL2 | 0.3708 | 1 | 0.7911 | 0.4382 | 0.1823 | 0.2911 | 0.3632 |
SL3 | 0.2883 | 0.7911 | 1 | 0.6131 | 0.2524 | 0.3968 | 0.5204 |
SL4 | 0.2367 | 0.4382 | 0.6131 | 1 | 0.2802 | 0.2422 | 0.4305 |
SL5 | 0.7048 | 0.1823 | 0.2524 | 0.2802 | 1 | 0.7869 | 0.7715 |
SL6 | 0.7114 | 0.2911 | 0.3968 | 0.2422 | 0.7869 | 1 | 0.8661 |
SL7 | 0.6511 | 0.3632 | 0.5204 | 0.4305 | 0.7715 | 0.8661 | 1 |
SL8 | 0.5508 | 0.2814 | 0.5322 | 0.3598 | 0.7366 | 0.7755 | 0.866 |
SL9 | 0.6249 | 0.1343 | 0.3413 | 0.3177 | 0.7371 | 0.6825 | 0.7056 |
SL10 | 0.6329 | 0.1861 | 0.333 | 0.3166 | 0.8037 | 0.6824 | 0.6958 |
SL11 | 0.6263 | 0.1344 | 0.3312 | 0.1822 | 0.7083 | 0.7387 | 0.7128 |
SL12 | 0.7017 | 0.2743 | 0.2875 | 0.0922 | 0.5979 | 0.6704 | 0.6335 |
SL8 | SL9 | SL10 | SL11 | SL12 | |
---|---|---|---|---|---|
SL1 | 0.5508 | 0.6249 | 0.6329 | 0.6263 | 0.7017 |
SL2 | 0.2814 | 0.1343 | 0.1861 | 0.1344 | 0.2743 |
SL3 | 0.5322 | 0.3413 | 0.333 | 0.3312 | 0.2875 |
SL4 | 0.3598 | 0.3177 | 0.3166 | 0.1822 | 0.0922 |
SL5 | 0.7366 | 0.7371 | 0.8037 | 0.7083 | 0.5979 |
SL6 | 0.7755 | 0.6825 | 0.6824 | 0.7387 | 0.6704 |
SL7 | 0.866 | 0.7056 | 0.6958 | 0.7128 | 0.6335 |
SL8 | 1 | 0.7112 | 0.7282 | 0.7088 | 0.5663 |
SL9 | 0.7112 | 1 | 0.8557 | 0.7802 | 0.5885 |
SL10 | 0.7282 | 0.8557 | 1 | 0.7819 | 0.5742 |
SL11 | 0.7088 | 0.7802 | 0.7819 | 1 | 0.736 |
SL12 | 0.5663 | 0.5885 | 0.5742 | 0.736 | 1 |
SL1 | SL2 | SL3 | SL4 | |
---|---|---|---|---|
UVWES1 | 0.1801 | 0.05897 | 0.1392 | 0.4563 |
UVWES4 | 0.09545 | 0.02533 | 0.2123 | 0.4215 |
UVWES8 | 0.1419 | 0.1778 | 0.3856 | 0.3608 |
UVWES12 | 0.2229 | 0.01605 | 0.1642 | 0.362 |
UVWES15 | 0.04964 | 0.03558 | 0.1592 | 0.5453 |
UVWES17 | -0.003427 | 0.4263 | 0.491 | 0.4616 |
SL5 | SL6 | SL7 | SL8 | SL9 | SL10 | |
---|---|---|---|---|---|---|
UVWES1 | 0.3857 | 0.2452 | 0.3338 | 0.3135 | 0.398 | 0.4199 |
UVWES4 | 0.2434 | 0.1087 | 0.3702 | 0.3248 | 0.2396 | 0.2633 |
UVWES8 | 0.2236 | 0.2284 | 0.3676 | 0.4897 | 0.3187 | 0.4092 |
UVWES12 | 0.1925 | 0.1953 | 0.3141 | 0.2964 | 0.3226 | 0.3055 |
UVWES15 | 0.1358 | 0.09999 | 0.2574 | 0.2342 | 0.207 | 0.1998 |
UVWES17 | 0.1065 | 0.1088 | 0.2521 | 0.2715 | 0.165 | 0.3524 |
SL11 | SL12 | |
---|---|---|
UVWES1 | 0.2438 | 0.2139 |
UVWES4 | 0.3051 | 0.2439 |
UVWES8 | 0.2884 | 0.2294 |
UVWES12 | 0.2448 | 0.06704 |
UVWES15 | 0.05293 | 0.1558 |
UVWES17 | 0.2074 | 0.0937 |
SL1 | SL2 | SL3 | SL4 | |
---|---|---|---|---|
UVWES3 | 0.2132 | 0.1484 | 0.1984 | 0.2957 |
UVWES6 | 0.1967 | 0.1787 | 0.09371 | 0.4128 |
UVWES9 | 0.3282 | 0.1334 | 0.4388 | 0.4118 |
UVWES11 | 0.1917 | 0.09858 | 0.228 | 0.418 |
UVWES14 | 0.1801 | 0.02068 | 0.1925 | 0.305 |
UVWES16 | -0.06557 | 0.1819 | 0.3733 | 0.2885 |
SL5 | SL6 | SL7 | SL8 | SL9 | SL10 | |
---|---|---|---|---|---|---|
UVWES3 | 0.2515 | 0.1258 | 0.2403 | 0.2643 | 0.2941 | 0.3034 |
UVWES6 | 0.159 | 0.136 | 0.1474 | 0.1418 | 0.02117 | 0.1262 |
UVWES9 | 0.3291 | 0.3642 | 0.5385 | 0.5265 | 0.5455 | 0.5034 |
UVWES11 | 0.3234 | 0.3522 | 0.4002 | 0.3849 | 0.3748 | 0.4075 |
UVWES14 | 0.2318 | 0.1828 | 0.3053 | 0.2988 | 0.3554 | 0.3414 |
UVWES16 | -0.04192 | 0.09867 | 0.102 | 0.182 | -0.1023 | -0.009363 |
SL11 | SL12 | |
---|---|---|
UVWES3 | 0.2383 | 0.3685 |
UVWES6 | -0.0896 | 0.07827 |
UVWES9 | 0.4122 | 0.1958 |
UVWES11 | 0.2797 | 0.06652 |
UVWES14 | 0.273 | 0.01917 |
UVWES16 | 0.07997 | 0.08368 |
p-value | Satisfacción Laboral | WorkEngagement | Rsq | |
---|---|---|---|---|
9 | 0.2108057 | SL1 | UVWES1 | 0.0324258 |
19 | 0.6841793 | SL2 | UVWES1 | 0.0034771 |
29 | 0.3349809 | SL3 | UVWES1 | 0.0193778 |
39 | 0.0008665 | SL4 | UVWES1 | 0.2082237 |
49 | 0.5096381 | SL1 | UVWES4 | 0.0091116 |
59 | 0.8614121 | SL2 | UVWES4 | 0.0006414 |
69 | 0.1389119 | SL3 | UVWES4 | 0.0450538 |
79 | 0.0023025 | SL4 | UVWES4 | 0.1776268 |
89 | 0.3256374 | SL1 | UVWES8 | 0.0201335 |
99 | 0.2167504 | SL2 | UVWES8 | 0.0316082 |
109 | 0.0056785 | SL3 | UVWES8 | 0.1487187 |
119 | 0.0100616 | SL4 | UVWES8 | 0.1301436 |
129 | 0.1196621 | SL1 | UVWES12 | 0.0497012 |
139 | 0.9119154 | SL2 | UVWES12 | 0.0002576 |
149 | 0.2544728 | SL3 | UVWES12 | 0.0269661 |
159 | 0.0097942 | SL4 | UVWES12 | 0.1310217 |
169 | 0.7320737 | SL1 | UVWES15 | 0.0024645 |
179 | 0.8062268 | SL2 | UVWES15 | 0.0012659 |
189 | 0.2696052 | SL3 | UVWES15 | 0.0253297 |
199 | 0.0000422 | SL4 | UVWES15 | 0.2973573 |
209 | 0.9811586 | SL1 | UVWES17 | 0.0000117 |
219 | 0.0020242 | SL2 | UVWES17 | 0.1817049 |
229 | 0.0002943 | SL3 | UVWES17 | 0.2410711 |
239 | 0.0007402 | SL4 | UVWES17 | 0.2130836 |
p-value | Satisfacción Laboral | WorkEngagement | Rsq | |
---|---|---|---|---|
9 | 0.0056747 | SL5 | UVWES1 | 0.1487404 |
19 | 0.0860534 | SL6 | UVWES1 | 0.0601442 |
29 | 0.0178502 | SL7 | UVWES1 | 0.1113957 |
39 | 0.0266147 | SL8 | UVWES1 | 0.0982987 |
49 | 0.0042005 | SL9 | UVWES1 | 0.1584348 |
59 | 0.0023992 | SL10 | UVWES1 | 0.1763215 |
69 | 0.0884858 | SL5 | UVWES4 | 0.0592538 |
79 | 0.4524838 | SL6 | UVWES4 | 0.0118115 |
89 | 0.0081414 | SL7 | UVWES4 | 0.1370386 |
99 | 0.0213504 | SL8 | UVWES4 | 0.1055255 |
109 | 0.0937751 | SL9 | UVWES4 | 0.0574033 |
119 | 0.0647162 | SL10 | UVWES4 | 0.0693083 |
129 | 0.1185637 | SL5 | UVWES8 | 0.0499903 |
139 | 0.1106756 | SL6 | UVWES8 | 0.0521547 |
149 | 0.0086336 | SL7 | UVWES8 | 0.1351294 |
159 | 0.0003069 | SL8 | UVWES8 | 0.2398132 |
169 | 0.0240809 | SL9 | UVWES8 | 0.1015791 |
179 | 0.0031713 | SL10 | UVWES8 | 0.1674389 |
189 | 0.1804209 | SL5 | UVWES12 | 0.0370640 |
199 | 0.1739812 | SL6 | UVWES12 | 0.0381609 |
209 | 0.0263145 | SL7 | UVWES12 | 0.0986706 |
219 | 0.0365865 | SL8 | UVWES12 | 0.0878750 |
229 | 0.0223272 | SL9 | UVWES12 | 0.1040586 |
239 | 0.0309914 | SL10 | UVWES12 | 0.0933087 |
249 | 0.3471651 | SL5 | UVWES15 | 0.0184328 |
259 | 0.4896507 | SL6 | UVWES15 | 0.0099973 |
269 | 0.0711597 | SL7 | UVWES15 | 0.0662447 |
279 | 0.1016509 | SL8 | UVWES15 | 0.0548423 |
289 | 0.1491354 | SL9 | UVWES15 | 0.0428622 |
299 | 0.1641283 | SL10 | UVWES15 | 0.0399303 |
309 | 0.4618484 | SL5 | UVWES17 | 0.0113327 |
319 | 0.4520188 | SL6 | UVWES17 | 0.0118357 |
329 | 0.0773200 | SL7 | UVWES17 | 0.0635735 |
339 | 0.0564896 | SL8 | UVWES17 | 0.0737127 |
349 | 0.2521152 | SL9 | UVWES17 | 0.0272316 |
359 | 0.0120877 | SL10 | UVWES17 | 0.1241547 |
p-value | Satisfacción Laboral | WorkEngagement | Rsq | |
---|---|---|---|---|
9 | 0.0879586 | SL11 | UVWES1 | 0.0594446 |
19 | 0.1357868 | SL12 | UVWES1 | 0.0457590 |
29 | 0.0311884 | SL11 | UVWES4 | 0.0931011 |
39 | 0.0878829 | SL12 | UVWES4 | 0.0594721 |
49 | 0.0422450 | SL11 | UVWES8 | 0.0831747 |
59 | 0.1090879 | SL12 | UVWES8 | 0.0526102 |
69 | 0.0865820 | SL11 | UVWES12 | 0.0599485 |
79 | 0.6436880 | SL12 | UVWES12 | 0.0044938 |
89 | 0.7150891 | SL11 | UVWES15 | 0.0028011 |
99 | 0.2798868 | SL12 | UVWES15 | 0.0242804 |
109 | 0.1483982 | SL11 | UVWES17 | 0.0430147 |
119 | 0.5174804 | SL12 | UVWES17 | 0.0087799 |
p-value | Satisfacción Laboral | WorkEngagement | Rsq | |
---|---|---|---|---|
9 | 0.1370367 | SL1 | UVWES3 | 0.0454748 |
19 | 0.3038183 | SL2 | UVWES3 | 0.0220126 |
29 | 0.1671477 | SL3 | UVWES3 | 0.0393758 |
39 | 0.0370835 | SL4 | UVWES3 | 0.0874336 |
49 | 0.1709911 | SL1 | UVWES6 | 0.0386858 |
59 | 0.2143700 | SL2 | UVWES6 | 0.0319324 |
69 | 0.5174455 | SL3 | UVWES6 | 0.0087813 |
79 | 0.0028900 | SL4 | UVWES6 | 0.1704025 |
89 | 0.0199825 | SL1 | UVWES9 | 0.1076967 |
99 | 0.3557175 | SL2 | UVWES9 | 0.0177954 |
109 | 0.0014336 | SL3 | UVWES9 | 0.1925587 |
119 | 0.0029619 | SL4 | UVWES9 | 0.1696187 |
129 | 0.1824337 | SL1 | UVWES11 | 0.0367301 |
139 | 0.4958074 | SL2 | UVWES11 | 0.0097181 |
149 | 0.1112488 | SL3 | UVWES11 | 0.0519919 |
159 | 0.0025259 | SL4 | UVWES11 | 0.1746885 |
169 | 0.2108057 | SL1 | UVWES14 | 0.0324258 |
179 | 0.8866666 | SL2 | UVWES14 | 0.0004275 |
189 | 0.1803775 | SL3 | UVWES14 | 0.0370712 |
199 | 0.0312802 | SL4 | UVWES14 | 0.0930048 |
209 | 0.6509895 | SL1 | UVWES16 | 0.0042990 |
219 | 0.2060352 | SL2 | UVWES16 | 0.0331015 |
229 | 0.0075776 | SL3 | UVWES16 | 0.1393706 |
239 | 0.0421908 | SL4 | UVWES16 | 0.0832166 |
p-value | Satisfacción Laboral | WorkEngagement | Rsq | |
---|---|---|---|---|
9 | 0.0780711 | SL5 | UVWES3 | 0.0632630 |
19 | 0.3839703 | SL6 | UVWES3 | 0.0158292 |
29 | 0.0927180 | SL7 | UVWES3 | 0.0577642 |
39 | 0.0635837 | SL8 | UVWES3 | 0.0698793 |
49 | 0.0381640 | SL9 | UVWES3 | 0.0864943 |
59 | 0.0322162 | SL10 | UVWES3 | 0.0920391 |
69 | 0.2701111 | SL5 | UVWES6 | 0.0252769 |
79 | 0.3463280 | SL6 | UVWES6 | 0.0184963 |
89 | 0.3071469 | SL7 | UVWES6 | 0.0217150 |
99 | 0.3260921 | SL8 | UVWES6 | 0.0200960 |
109 | 0.8839844 | SL9 | UVWES6 | 0.0004481 |
119 | 0.3825500 | SL10 | UVWES6 | 0.0159232 |
129 | 0.0196199 | SL5 | UVWES9 | 0.1082970 |
139 | 0.0093091 | SL6 | UVWES9 | 0.1326769 |
149 | 0.0000549 | SL7 | UVWES9 | 0.2899739 |
159 | 0.0000859 | SL8 | UVWES9 | 0.2771680 |
169 | 0.0000419 | SL9 | UVWES9 | 0.2975889 |
179 | 0.0001941 | SL10 | UVWES9 | 0.2534392 |
189 | 0.0219552 | SL5 | UVWES11 | 0.1046096 |
199 | 0.0121394 | SL6 | UVWES11 | 0.1240154 |
209 | 0.0039791 | SL7 | UVWES11 | 0.1601739 |
219 | 0.0057774 | SL8 | UVWES11 | 0.1481606 |
229 | 0.0073259 | SL9 | UVWES11 | 0.1404677 |
239 | 0.0033128 | SL10 | UVWES11 | 0.1660441 |
249 | 0.1052654 | SL5 | UVWES14 | 0.0537366 |
259 | 0.2038366 | SL6 | UVWES14 | 0.0334190 |
269 | 0.0310831 | SL7 | UVWES14 | 0.0932120 |
279 | 0.0350695 | SL8 | UVWES14 | 0.0892606 |
289 | 0.0113107 | SL9 | UVWES14 | 0.1263249 |
299 | 0.0152590 | SL10 | UVWES14 | 0.1165338 |
309 | 0.7725189 | SL5 | UVWES16 | 0.0017577 |
319 | 0.4953941 | SL6 | UVWES16 | 0.0097367 |
329 | 0.4808839 | SL7 | UVWES16 | 0.0104050 |
339 | 0.2058583 | SL8 | UVWES16 | 0.0331269 |
349 | 0.4794517 | SL9 | UVWES16 | 0.0104727 |
359 | 0.9485474 | SL10 | UVWES16 | 0.0000877 |
p-value | Satisfacción Laboral | WorkEngagement | Rsq | |
---|---|---|---|---|
9 | 0.0956134 | SL11 | UVWES3 | 0.0567857 |
19 | 0.0084534 | SL12 | UVWES3 | 0.1358156 |
29 | 0.5360325 | SL11 | UVWES6 | 0.0080290 |
39 | 0.5890025 | SL12 | UVWES6 | 0.0061261 |
49 | 0.0029380 | SL11 | UVWES9 | 0.1698779 |
59 | 0.1730090 | SL12 | UVWES9 | 0.0383305 |
69 | 0.0491796 | SL11 | UVWES11 | 0.0782182 |
79 | 0.6462538 | SL12 | UVWES11 | 0.0044248 |
89 | 0.0551086 | SL11 | UVWES14 | 0.0745164 |
99 | 0.8948532 | SL12 | UVWES14 | 0.0003677 |
109 | 0.5809262 | SL11 | UVWES16 | 0.0063946 |
119 | 0.5634338 | SL12 | UVWES16 | 0.0070022 |
p-value | Satisfacción Laboral | WorkEngagement | Rsq | |
---|---|---|---|---|
9 | 0.1849866 | SL1 | UVWES2 | 0.0363126 |
19 | 0.0535279 | SL2 | UVWES2 | 0.0754619 |
29 | 0.0494162 | SL3 | UVWES2 | 0.0780620 |
39 | 0.1631533 | SL4 | UVWES2 | 0.0401118 |
49 | 0.0065971 | SL1 | UVWES5 | 0.1438659 |
59 | 0.7824819 | SL2 | UVWES5 | 0.0016033 |
69 | 0.3041910 | SL3 | UVWES5 | 0.0219791 |
79 | 0.2634719 | SL4 | UVWES5 | 0.0259792 |
89 | 0.6604711 | SL1 | UVWES7 | 0.0040537 |
99 | 0.9390777 | SL2 | UVWES7 | 0.0001230 |
109 | 0.2821422 | SL3 | UVWES7 | 0.0240565 |
119 | 0.0012898 | SL4 | UVWES7 | 0.1958654 |
129 | 0.2134110 | SL1 | UVWES10 | 0.0320643 |
139 | 0.9359143 | SL2 | UVWES10 | 0.0001361 |
149 | 0.2718075 | SL3 | UVWES10 | 0.0251008 |
159 | 0.0283522 | SL4 | UVWES10 | 0.0962254 |
169 | 0.0518030 | SL1 | UVWES13 | 0.0765269 |
179 | 0.4380125 | SL2 | UVWES13 | 0.0125821 |
189 | 0.0116054 | SL3 | UVWES13 | 0.1254850 |
199 | 0.0001859 | SL4 | UVWES13 | 0.2547160 |
p-value | Satisfacción Laboral | WorkEngagement | Rsq | |
---|---|---|---|---|
9 | 0.3761448 | SL5 | UVWES2 | 0.0163534 |
19 | 0.0554801 | SL6 | UVWES2 | 0.0742981 |
29 | 0.0928752 | SL7 | UVWES2 | 0.0577102 |
39 | 0.1325191 | SL8 | UVWES2 | 0.0465155 |
49 | 0.0190312 | SL9 | UVWES2 | 0.1092958 |
59 | 0.0862788 | SL10 | UVWES2 | 0.0600606 |
69 | 0.0000086 | SL5 | UVWES5 | 0.3408636 |
79 | 0.0008105 | SL6 | UVWES5 | 0.2102860 |
89 | 0.0000568 | SL7 | UVWES5 | 0.2889703 |
99 | 0.0016791 | SL8 | UVWES5 | 0.1875970 |
109 | 0.0002709 | SL9 | UVWES5 | 0.2435439 |
119 | 0.0003004 | SL10 | UVWES5 | 0.2404483 |
129 | 0.0939096 | SL5 | UVWES7 | 0.0573576 |
139 | 0.1461395 | SL6 | UVWES7 | 0.0434870 |
149 | 0.1597385 | SL7 | UVWES7 | 0.0407571 |
159 | 0.1960270 | SL8 | UVWES7 | 0.0345793 |
169 | 0.0691402 | SL9 | UVWES7 | 0.0671729 |
179 | 0.0679088 | SL10 | UVWES7 | 0.0677528 |
189 | 0.0054633 | SL5 | UVWES10 | 0.1499669 |
199 | 0.0907621 | SL6 | UVWES10 | 0.0584435 |
209 | 0.0028636 | SL7 | UVWES10 | 0.1706947 |
219 | 0.0078765 | SL8 | UVWES10 | 0.1381139 |
229 | 0.0015702 | SL9 | UVWES10 | 0.1897057 |
239 | 0.0153877 | SL10 | UVWES10 | 0.1162586 |
249 | 0.0262324 | SL5 | UVWES13 | 0.0987730 |
259 | 0.0459297 | SL6 | UVWES13 | 0.0804460 |
269 | 0.0011842 | SL7 | UVWES13 | 0.1985323 |
279 | 0.0116039 | SL8 | UVWES13 | 0.1254891 |
289 | 0.0047200 | SL9 | UVWES13 | 0.1546837 |
299 | 0.0230991 | SL10 | UVWES13 | 0.1029441 |
p-value | Satisfacción Laboral | WorkEngagement | Rsq | |
---|---|---|---|---|
9 | 0.0556605 | SL11 | UVWES2 | 0.0741928 |
19 | 0.0385244 | SL12 | UVWES2 | 0.0861870 |
29 | 0.0000451 | SL11 | UVWES5 | 0.2954852 |
39 | 0.0031759 | SL12 | UVWES5 | 0.1673927 |
49 | 0.1304985 | SL11 | UVWES7 | 0.0469935 |
59 | 0.5591565 | SL12 | UVWES7 | 0.0071563 |
69 | 0.0351296 | SL11 | UVWES10 | 0.0892046 |
79 | 0.0590336 | SL12 | UVWES10 | 0.0722838 |
89 | 0.0202631 | SL11 | UVWES13 | 0.1072395 |
99 | 0.3165041 | SL12 | UVWES13 | 0.0208999 |
``` |