Study 2.2: Semantic decision

Table 12 presents the results of the informative prior model, Table 13 those of the weakly-informative prior model, and Table 14 those of the diffuse prior model.

Code 

# Rename effects in plain language and specify the random slopes
# (if any) for each effect, in the footnote. For this purpose, 
# superscripts are added to the names of the appropriate effects.
# 
# In the interactions below, word-level variables are presented 
# first for the sake of consistency (the order does not affect 
# the results in any way). Also in the interactions, double 
# colons are used to inform the 'bayesian_model_table' function 
# that the two terms in the interaction must be split into two 
# lines.

rownames(semanticdecision_summary_informativepriors_exgaussian$fixed)[
  rownames(semanticdecision_summary_informativepriors_exgaussian$fixed) == 
    'z_information_uptake'] = 'Information uptake'

rownames(semanticdecision_summary_informativepriors_exgaussian$fixed)[
  rownames(semanticdecision_summary_informativepriors_exgaussian$fixed) == 
    'z_vocabulary_size'] = 'Vocabulary size <sup>a</sup>'

rownames(semanticdecision_summary_informativepriors_exgaussian$fixed)[
  rownames(semanticdecision_summary_informativepriors_exgaussian$fixed) == 
    'z_recoded_participant_gender'] = 'Gender <sup>a</sup>'

rownames(semanticdecision_summary_informativepriors_exgaussian$fixed)[
  rownames(semanticdecision_summary_informativepriors_exgaussian$fixed) == 
    'z_word_frequency'] = 'Word frequency'

rownames(semanticdecision_summary_informativepriors_exgaussian$fixed)[
  rownames(semanticdecision_summary_informativepriors_exgaussian$fixed) == 
    'z_orthographic_Levenshtein_distance'] = 'Orthographic Levenshtein distance'

rownames(semanticdecision_summary_informativepriors_exgaussian$fixed)[
  rownames(semanticdecision_summary_informativepriors_exgaussian$fixed) == 
    'z_word_concreteness'] = 'Word concreteness'

rownames(semanticdecision_summary_informativepriors_exgaussian$fixed)[
  rownames(semanticdecision_summary_informativepriors_exgaussian$fixed) == 
    'z_word_cooccurrence'] = "Word co-occurrence <sup>b</sup>"

rownames(semanticdecision_summary_informativepriors_exgaussian$fixed)[
  rownames(semanticdecision_summary_informativepriors_exgaussian$fixed) == 
    'z_visual_rating'] = 'Visual strength <sup>b</sup>'

rownames(semanticdecision_summary_informativepriors_exgaussian$fixed)[
  rownames(semanticdecision_summary_informativepriors_exgaussian$fixed) == 
    'z_word_concreteness:z_vocabulary_size'] = 
  'Word concreteness : Vocabulary size'

rownames(semanticdecision_summary_informativepriors_exgaussian$fixed)[
  rownames(semanticdecision_summary_informativepriors_exgaussian$fixed) == 
    'z_word_concreteness:z_recoded_participant_gender'] = 
  'Word concreteness : Gender'

rownames(semanticdecision_summary_informativepriors_exgaussian$fixed)[
  rownames(semanticdecision_summary_informativepriors_exgaussian$fixed) == 
    'z_information_uptake:z_word_cooccurrence'] = 
  "Word co-occurrence : Information uptake"

rownames(semanticdecision_summary_informativepriors_exgaussian$fixed)[
  rownames(semanticdecision_summary_informativepriors_exgaussian$fixed) == 
    'z_information_uptake:z_visual_rating'] = 
  'Visual strength : Information uptake'

rownames(semanticdecision_summary_informativepriors_exgaussian$fixed)[
  rownames(semanticdecision_summary_informativepriors_exgaussian$fixed) == 
    'z_vocabulary_size:z_word_cooccurrence'] = 
  "Word co-occurrence : Vocabulary size"

rownames(semanticdecision_summary_informativepriors_exgaussian$fixed)[
  rownames(semanticdecision_summary_informativepriors_exgaussian$fixed) == 
    'z_vocabulary_size:z_visual_rating'] = 
  'Visual strength : Vocabulary size'

rownames(semanticdecision_summary_informativepriors_exgaussian$fixed)[
  rownames(semanticdecision_summary_informativepriors_exgaussian$fixed) == 
    'z_recoded_participant_gender:z_word_cooccurrence'] = 
  "Word co-occurrence : Gender"

rownames(semanticdecision_summary_informativepriors_exgaussian$fixed)[
  rownames(semanticdecision_summary_informativepriors_exgaussian$fixed) == 
    'z_recoded_participant_gender:z_visual_rating'] = 
  'Visual strength : Gender'


# Create table (using custom function from the 'R_functions' folder)
bayesian_model_table(
  semanticdecision_summary_informativepriors_exgaussian, 
  order_effects = c('(Intercept)',
                    'Information uptake',
                    'Vocabulary size <sup>a</sup>',
                    'Gender <sup>a</sup>',
                    'Word frequency',
                    'Orthographic Levenshtein distance',
                    'Word concreteness',
                    "Word co-occurrence <sup>b</sup>",
                    'Visual strength <sup>b</sup>',
                    'Word concreteness : Vocabulary size',
                    'Word concreteness : Gender',
                    "Word co-occurrence : Information uptake",
                    'Visual strength : Information uptake',
                    "Word co-occurrence : Vocabulary size",
                    'Visual strength : Vocabulary size',
                    "Word co-occurrence : Gender",
                    'Visual strength : Gender'),
  interaction_symbol_x = TRUE,
  caption = 'Informative prior model for the semantic decision study.') %>%
  
  # Group predictors under headings
  pack_rows('Individual differences', 2, 4) %>% 
  pack_rows('Lexicosemantic covariates', 5, 7) %>% 
  pack_rows('Semantic variables', 8, 9) %>% 
  pack_rows('Interactions', 10, 17) %>% 
  
  # Apply white background to override default shading in HTML output
  row_spec(1:17, background = 'white') %>%
  
  # Highlight covariates
  row_spec(c(2, 5:7, 10:13), background = '#FFFFF1') %>%
  
  # Format
  kable_classic(full_width = FALSE, html_font = 'Cambria') %>%
  
  # Footnote describing abbreviations, random slopes, etc. 
  footnote(escape = FALSE, threeparttable = TRUE, 
           # The <p> below is used to enter a margin above the footnote 
           general_title = '<p style="margin-top: 10px;"></p>', 
           general = paste('*Note*. &beta; = Estimate based on $z$-scored predictors; *SE* = standard error;',
                           'CrI = credible interval. Yellow rows contain covariates. <br>', 
                           '<sup>a</sup> By-word random slopes were included for this effect.',
                           '<sup>b</sup> By-participant random slopes were included for this effect.'))
Table 12: Informative prior model for the semantic decision study.
β SE 95% CrI \(\widehat{R}\)
(Intercept) 0.14 0.42 [0.00, 1.72] 1.31
Individual differences
Information uptake 0.03 0.08 [-0.01, 0.31] 1.31
Vocabulary size a 0.18 0.46 [0.00, 1.44] 1.31
Gender a -0.12 0.39 [-1.56, 0.02] 1.31
Lexicosemantic covariates
Word frequency -0.18 0.31 [-1.34, -0.07] 1.30
Orthographic Levenshtein distance 0.06 0.56 [-1.14, 1.94] 1.41
Word concreteness 0.00 0.26 [-0.08, 1.01] 1.30
Semantic variables
Word co-occurrence b -0.05 0.23 [-0.87, 0.40] 1.41
Visual strength b -0.20 0.49 [-1.52, -0.01] 1.31
Interactions
Word concreteness × Vocabulary size 0.02 0.55 [-1.24, 1.83] 1.42
Word concreteness × Gender 0.07 0.40 [-0.31, 1.58] 1.42
Word co-occurrence × Information uptake -0.06 0.19 [-0.70, 0.02] 1.31
Visual strength × Information uptake -0.15 0.46 [-1.79, 0.02] 1.30
Word co-occurrence × Vocabulary size -0.04 0.55 [-1.92, 1.11] 1.42
Visual strength × Vocabulary size 0.15 0.38 [0.00, 1.27] 1.30
Word co-occurrence × Gender 0.00 0.26 [-0.78, 0.68] 1.41
Visual strength × Gender 0.18 0.49 [-0.01, 1.66] 1.30

Note. β = Estimate based on \(z\)-scored predictors; SE = standard error; CrI = credible interval. Yellow rows contain covariates.
a By-word random slopes were included for this effect. b By-participant random slopes were included for this effect.
Code 

# Rename effects in plain language and specify the random slopes
# (if any) for each effect, in the footnote. For this purpose, 
# superscripts are added to the names of the appropriate effects.
# 
# In the interactions below, word-level variables are presented 
# first for the sake of consistency (the order does not affect 
# the results in any way). Also in the interactions, double 
# colons are used to inform the 'bayesian_model_table' function 
# that the two terms in the interaction must be split into two 
# lines.

rownames(semanticdecision_summary_weaklyinformativepriors_exgaussian$fixed)[
  rownames(semanticdecision_summary_weaklyinformativepriors_exgaussian$fixed) == 
    'z_information_uptake'] = 'Information uptake'

rownames(semanticdecision_summary_weaklyinformativepriors_exgaussian$fixed)[
  rownames(semanticdecision_summary_weaklyinformativepriors_exgaussian$fixed) == 
    'z_vocabulary_size'] = 'Vocabulary size <sup>a</sup>'

rownames(semanticdecision_summary_weaklyinformativepriors_exgaussian$fixed)[
  rownames(semanticdecision_summary_weaklyinformativepriors_exgaussian$fixed) == 
    'z_recoded_participant_gender'] = 'Gender <sup>a</sup>'

rownames(semanticdecision_summary_weaklyinformativepriors_exgaussian$fixed)[
  rownames(semanticdecision_summary_weaklyinformativepriors_exgaussian$fixed) == 
    'z_word_frequency'] = 'Word frequency'

rownames(semanticdecision_summary_weaklyinformativepriors_exgaussian$fixed)[
  rownames(semanticdecision_summary_weaklyinformativepriors_exgaussian$fixed) == 
    'z_orthographic_Levenshtein_distance'] = 'Orthographic Levenshtein distance'

rownames(semanticdecision_summary_weaklyinformativepriors_exgaussian$fixed)[
  rownames(semanticdecision_summary_weaklyinformativepriors_exgaussian$fixed) == 
    'z_word_concreteness'] = 'Word concreteness'

rownames(semanticdecision_summary_weaklyinformativepriors_exgaussian$fixed)[
  rownames(semanticdecision_summary_weaklyinformativepriors_exgaussian$fixed) == 
    'z_word_cooccurrence'] = "Word co-occurrence <sup>b</sup>"

rownames(semanticdecision_summary_weaklyinformativepriors_exgaussian$fixed)[
  rownames(semanticdecision_summary_weaklyinformativepriors_exgaussian$fixed) == 
    'z_visual_rating'] = 'Visual strength <sup>b</sup>'

rownames(semanticdecision_summary_weaklyinformativepriors_exgaussian$fixed)[
  rownames(semanticdecision_summary_weaklyinformativepriors_exgaussian$fixed) == 
    'z_word_concreteness:z_vocabulary_size'] = 
  'Word concreteness : Vocabulary size'

rownames(semanticdecision_summary_weaklyinformativepriors_exgaussian$fixed)[
  rownames(semanticdecision_summary_weaklyinformativepriors_exgaussian$fixed) == 
    'z_word_concreteness:z_recoded_participant_gender'] = 
  'Word concreteness : Gender'

rownames(semanticdecision_summary_weaklyinformativepriors_exgaussian$fixed)[
  rownames(semanticdecision_summary_weaklyinformativepriors_exgaussian$fixed) == 
    'z_information_uptake:z_word_cooccurrence'] = 
  "Word co-occurrence : Information uptake"

rownames(semanticdecision_summary_weaklyinformativepriors_exgaussian$fixed)[
  rownames(semanticdecision_summary_weaklyinformativepriors_exgaussian$fixed) == 
    'z_information_uptake:z_visual_rating'] = 
  'Visual strength : Information uptake'

rownames(semanticdecision_summary_weaklyinformativepriors_exgaussian$fixed)[
  rownames(semanticdecision_summary_weaklyinformativepriors_exgaussian$fixed) == 
    'z_vocabulary_size:z_word_cooccurrence'] = 
  "Word co-occurrence : Vocabulary size"

rownames(semanticdecision_summary_weaklyinformativepriors_exgaussian$fixed)[
  rownames(semanticdecision_summary_weaklyinformativepriors_exgaussian$fixed) == 
    'z_vocabulary_size:z_visual_rating'] = 
  'Visual strength : Vocabulary size'

rownames(semanticdecision_summary_weaklyinformativepriors_exgaussian$fixed)[
  rownames(semanticdecision_summary_weaklyinformativepriors_exgaussian$fixed) == 
    'z_recoded_participant_gender:z_word_cooccurrence'] = 
  "Word co-occurrence : Gender"

rownames(semanticdecision_summary_weaklyinformativepriors_exgaussian$fixed)[
  rownames(semanticdecision_summary_weaklyinformativepriors_exgaussian$fixed) == 
    'z_recoded_participant_gender:z_visual_rating'] = 
  'Visual strength : Gender'


# Create table (using custom function from the 'R_functions' folder)
bayesian_model_table(
  semanticdecision_summary_weaklyinformativepriors_exgaussian, 
  order_effects = c('(Intercept)',
                    'Information uptake',
                    'Vocabulary size <sup>a</sup>',
                    'Gender <sup>a</sup>',
                    'Word frequency',
                    'Orthographic Levenshtein distance',
                    'Word concreteness',
                    "Word co-occurrence <sup>b</sup>",
                    'Visual strength <sup>b</sup>',
                    'Word concreteness : Vocabulary size',
                    'Word concreteness : Gender',
                    "Word co-occurrence : Information uptake",
                    'Visual strength : Information uptake',
                    "Word co-occurrence : Vocabulary size",
                    'Visual strength : Vocabulary size',
                    "Word co-occurrence : Gender",
                    'Visual strength : Gender'),
  interaction_symbol_x = TRUE,
  caption = 'Weakly-informative prior model for the semantic decision study.') %>%
  
  # Group predictors under headings
  pack_rows('Individual differences', 2, 4) %>% 
  pack_rows('Lexicosemantic covariates', 5, 7) %>% 
  pack_rows('Semantic variables', 8, 9) %>% 
  pack_rows('Interactions', 10, 17) %>%  
  
  # Apply white background to override default shading in HTML output
  row_spec(1:17, background = 'white') %>%
  
  # Highlight covariates
  row_spec(c(2, 5:7, 10:13), background = '#FFFFF1') %>%
  
  # Format
  kable_classic(full_width = FALSE, html_font = 'Cambria') %>%
  
  # Footnote describing abbreviations, random slopes, etc. 
  footnote(escape = FALSE, threeparttable = TRUE, 
           # The <p> below is used to enter a margin above the footnote 
           general_title = '<p style="margin-top: 10px;"></p>', 
           general = paste('*Note*. &beta; = Estimate based on $z$-scored predictors; *SE* = standard error;',
                           'CrI = credible interval. Yellow rows contain covariates. <br>', 
                           '<sup>a</sup> By-word random slopes were included for this effect.',
                           '<sup>b</sup> By-participant random slopes were included for this effect.'))
Table 13: Weakly-informative prior model for the semantic decision study.
β SE 95% CrI \(\widehat{R}\)
(Intercept) 0.14 0.42 [0.00, 1.72] 1.31
Individual differences
Information uptake 0.03 0.08 [-0.01, 0.31] 1.31
Vocabulary size a 0.18 0.46 [0.00, 1.44] 1.31
Gender a -0.12 0.39 [-1.56, 0.02] 1.30
Lexicosemantic covariates
Word frequency -0.18 0.31 [-1.34, -0.07] 1.31
Orthographic Levenshtein distance 0.06 0.56 [-1.14, 1.94] 1.40
Word concreteness 0.00 0.26 [-0.08, 1.01] 1.30
Semantic variables
Word co-occurrence b -0.05 0.23 [-0.87, 0.40] 1.41
Visual strength b -0.20 0.49 [-1.52, -0.01] 1.31
Interactions
Word concreteness × Vocabulary size 0.02 0.55 [-1.24, 1.83] 1.41
Word concreteness × Gender 0.07 0.40 [-0.31, 1.58] 1.42
Word co-occurrence × Information uptake -0.06 0.19 [-0.70, 0.02] 1.31
Visual strength × Information uptake -0.15 0.46 [-1.79, 0.02] 1.31
Word co-occurrence × Vocabulary size -0.04 0.55 [-1.92, 1.11] 1.42
Visual strength × Vocabulary size 0.15 0.38 [0.00, 1.28] 1.30
Word co-occurrence × Gender 0.00 0.26 [-0.78, 0.68] 1.41
Visual strength × Gender 0.18 0.49 [-0.01, 1.66] 1.31

Note. β = Estimate based on \(z\)-scored predictors; SE = standard error; CrI = credible interval. Yellow rows contain covariates.
a By-word random slopes were included for this effect. b By-participant random slopes were included for this effect.
Code 

# Rename effects in plain language and specify the random slopes
# (if any) for each effect, in the footnote. For this purpose, 
# superscripts are added to the names of the appropriate effects.
# 
# In the interactions below, word-level variables are presented 
# first for the sake of consistency (the order does not affect 
# the results in any way). Also in the interactions, double 
# colons are used to inform the 'bayesian_model_table' function 
# that the two terms in the interaction must be split into two 
# lines.

rownames(semanticdecision_summary_diffusepriors_exgaussian$fixed)[
  rownames(semanticdecision_summary_diffusepriors_exgaussian$fixed) == 
    'z_information_uptake'] = 'Information uptake'

rownames(semanticdecision_summary_diffusepriors_exgaussian$fixed)[
  rownames(semanticdecision_summary_diffusepriors_exgaussian$fixed) == 
    'z_vocabulary_size'] = 'Vocabulary size <sup>a</sup>'

rownames(semanticdecision_summary_diffusepriors_exgaussian$fixed)[
  rownames(semanticdecision_summary_diffusepriors_exgaussian$fixed) == 
    'z_recoded_participant_gender'] = 'Gender <sup>a</sup>'

rownames(semanticdecision_summary_diffusepriors_exgaussian$fixed)[
  rownames(semanticdecision_summary_diffusepriors_exgaussian$fixed) == 
    'z_word_frequency'] = 'Word frequency'

rownames(semanticdecision_summary_diffusepriors_exgaussian$fixed)[
  rownames(semanticdecision_summary_diffusepriors_exgaussian$fixed) == 
    'z_orthographic_Levenshtein_distance'] = 'Orthographic Levenshtein distance'

rownames(semanticdecision_summary_diffusepriors_exgaussian$fixed)[
  rownames(semanticdecision_summary_diffusepriors_exgaussian$fixed) == 
    'z_word_concreteness'] = 'Word concreteness'

rownames(semanticdecision_summary_diffusepriors_exgaussian$fixed)[
  rownames(semanticdecision_summary_diffusepriors_exgaussian$fixed) == 
    'z_word_cooccurrence'] = "Word co-occurrence <sup>b</sup>"

rownames(semanticdecision_summary_diffusepriors_exgaussian$fixed)[
  rownames(semanticdecision_summary_diffusepriors_exgaussian$fixed) == 
    'z_visual_rating'] = 'Visual strength <sup>b</sup>'

rownames(semanticdecision_summary_diffusepriors_exgaussian$fixed)[
  rownames(semanticdecision_summary_diffusepriors_exgaussian$fixed) == 
    'z_word_concreteness:z_vocabulary_size'] = 
  'Word concreteness : Vocabulary size'

rownames(semanticdecision_summary_diffusepriors_exgaussian$fixed)[
  rownames(semanticdecision_summary_diffusepriors_exgaussian$fixed) == 
    'z_word_concreteness:z_recoded_participant_gender'] = 
  'Word concreteness : Gender'

rownames(semanticdecision_summary_diffusepriors_exgaussian$fixed)[
  rownames(semanticdecision_summary_diffusepriors_exgaussian$fixed) == 
    'z_information_uptake:z_word_cooccurrence'] = 
  "Word co-occurrence : Information uptake"

rownames(semanticdecision_summary_diffusepriors_exgaussian$fixed)[
  rownames(semanticdecision_summary_diffusepriors_exgaussian$fixed) == 
    'z_information_uptake:z_visual_rating'] = 
  'Visual strength : Information uptake'

rownames(semanticdecision_summary_diffusepriors_exgaussian$fixed)[
  rownames(semanticdecision_summary_diffusepriors_exgaussian$fixed) == 
    'z_vocabulary_size:z_word_cooccurrence'] = 
  "Word co-occurrence : Vocabulary size"

rownames(semanticdecision_summary_diffusepriors_exgaussian$fixed)[
  rownames(semanticdecision_summary_diffusepriors_exgaussian$fixed) == 
    'z_vocabulary_size:z_visual_rating'] = 
  'Visual strength : Vocabulary size'

rownames(semanticdecision_summary_diffusepriors_exgaussian$fixed)[
  rownames(semanticdecision_summary_diffusepriors_exgaussian$fixed) == 
    'z_recoded_participant_gender:z_word_cooccurrence'] = 
  "Word co-occurrence : Gender"

rownames(semanticdecision_summary_diffusepriors_exgaussian$fixed)[
  rownames(semanticdecision_summary_diffusepriors_exgaussian$fixed) == 
    'z_recoded_participant_gender:z_visual_rating'] = 
  'Visual strength : Gender'


# Create table (using custom function from the 'R_functions' folder)
bayesian_model_table(
  semanticdecision_summary_diffusepriors_exgaussian, 
  order_effects = c('(Intercept)',
                    'Information uptake',
                    'Vocabulary size <sup>a</sup>',
                    'Gender <sup>a</sup>',
                    'Word frequency',
                    'Orthographic Levenshtein distance',
                    'Word concreteness',
                    "Word co-occurrence <sup>b</sup>",
                    'Visual strength <sup>b</sup>',
                    'Word concreteness : Vocabulary size',
                    'Word concreteness : Gender',
                    "Word co-occurrence : Information uptake",
                    'Visual strength : Information uptake',
                    "Word co-occurrence : Vocabulary size",
                    'Visual strength : Vocabulary size',
                    "Word co-occurrence : Gender",
                    'Visual strength : Gender'),
  interaction_symbol_x = TRUE,
  caption = 'Diffuse prior model for the semantic decision study.') %>%
  
  # Group predictors under headings
  pack_rows('Individual differences', 2, 4) %>% 
  pack_rows('Lexicosemantic covariates', 5, 7) %>% 
  pack_rows('Semantic variables', 8, 9) %>% 
  pack_rows('Interactions', 10, 17) %>%  
  
  # Apply white background to override default shading in HTML output
  row_spec(1:17, background = 'white') %>%
  
  # Highlight covariates
  row_spec(c(2, 5:7, 10:13), background = '#FFFFF1') %>%
  
  # Format
  kable_classic(full_width = FALSE, html_font = 'Cambria') %>%
  
  # Footnote describing abbreviations, random slopes, etc. 
  footnote(escape = FALSE, threeparttable = TRUE, 
           # The <p> below is used to enter a margin above the footnote 
           general_title = '<p style="margin-top: 10px;"></p>', 
           general = paste('*Note*. &beta; = Estimate based on $z$-scored predictors; *SE* = standard error;',
                           'CrI = credible interval. Yellow rows contain covariates. <br>', 
                           '<sup>a</sup> By-word random slopes were included for this effect.',
                           '<sup>b</sup> By-participant random slopes were included for this effect.'))
Table 14: Diffuse prior model for the semantic decision study.
β SE 95% CrI \(\widehat{R}\)
(Intercept) 0.14 0.42 [0.00, 1.72] 1.31
Individual differences
Information uptake 0.03 0.08 [-0.01, 0.31] 1.30
Vocabulary size a 0.18 0.46 [0.00, 1.44] 1.30
Gender a -0.12 0.39 [-1.56, 0.02] 1.31
Lexicosemantic covariates
Word frequency -0.18 0.31 [-1.34, -0.07] 1.30
Orthographic Levenshtein distance 0.06 0.56 [-1.14, 1.94] 1.41
Word concreteness 0.00 0.26 [-0.08, 1.01] 1.30
Semantic variables
Word co-occurrence b -0.05 0.23 [-0.87, 0.40] 1.41
Visual strength b -0.20 0.49 [-1.52, -0.01] 1.31
Interactions
Word concreteness × Vocabulary size 0.02 0.55 [-1.24, 1.83] 1.41
Word concreteness × Gender 0.07 0.40 [-0.31, 1.58] 1.41
Word co-occurrence × Information uptake -0.06 0.19 [-0.70, 0.02] 1.31
Visual strength × Information uptake -0.15 0.46 [-1.79, 0.02] 1.30
Word co-occurrence × Vocabulary size -0.04 0.55 [-1.92, 1.11] 1.41
Visual strength × Vocabulary size 0.15 0.38 [0.00, 1.27] 1.30
Word co-occurrence × Gender 0.00 0.26 [-0.78, 0.68] 1.42
Visual strength × Gender 0.18 0.49 [-0.01, 1.66] 1.30

Note. β = Estimate based on \(z\)-scored predictors; SE = standard error; CrI = credible interval. Yellow rows contain covariates.
a By-word random slopes were included for this effect. b By-participant random slopes were included for this effect.

Figure 68 presents the posterior distribution of each effect in each model. The frequentist estimates are also shown to facilitate the comparison.

Code 

# Run plot through source() rather than directly in this R Markdown document
# to preserve the format.

source('semanticdecision/frequentist_bayesian_plots/semanticdecision_frequentist_bayesian_plots.R',
       local = TRUE)

include_graphics(
  paste0(
    getwd(),  # Circumvent illegal characters in file path
    '/semanticdecision/frequentist_bayesian_plots/plots/semanticdecision_frequentist_bayesian_plot_allpriors_exgaussian.pdf'
  ))

Figure 68: Estimates from the frequentist analysis (in red) and from the Bayesian analysis (in blue) for the semantic decision study, in each model. The frequentist means (represented by points) are flanked by 95% confidence intervals. The Bayesian means (represented by vertical lines) are flanked by 95% credible intervals in light blue (in some cases, the interval is occluded by the bar of the mean).


Pablo Bernabeu, 2022. Licence: CC BY 4.0.
Thesis: https://doi.org/10.17635/lancaster/thesis/1795.

Online book created using the R package bookdown.