2.5 Mis-Specification Analyis (MSA)

To trust inferences drawn from econometric analyses, one must check that the underlying assumptions are satisfied. (Hendry and Nielsen 2007)

• https://stats.stackexchange.com/questions/tagged/diagnostic Diagnostic measures (such as residuals or some summary statistics calculated from residuals) are used to evaluate some aspect of quality of model fit to data.

2.5.1 Normality

Analyse Residuals Graphically

• Interpreting plot.lm(), CrossValidated
• section 1.5.1 model fitting and model checking in (Wood 2017).
• Regression diagnostic plots, Data Analysis in the Geosciences, Steven Holland

For example, the following four plots can be used to check the plausibility of normality assumptions:

• The upper left plot shows residuals against fitted values of mods_recs[[1]]. It is hard to trust indication the flat trending line because there are few data points with low fitted values. The variance seems to be stable when fitted values are high. The assumption of homoskedasticity is tested formally in section 4.
• Data points 36, 241 and 163 are mentioned in all but the lower right plots. They are examined in section 6.
• The assumption of conditional normality looks reasonable according to the upper right Q-Q plot. A formal Jarque-Bera test is performed later this section to examine this assumption in a quantitative manner.

Jarque-Bera Test (test-JB)

The assumption of conditional normality is justified by JB test.

mods_recs[[1]] %>% test_jb(dat_recs) %>% tab_ti()

whi	stat	df1	df2	p_value	prob	if_reject
Jarque-Bera	2.067	2	298	0.3557	0.05	FALSE

Address the Normality Problem

• Look at the data.
• Change the distributional assumption.
• Check the robustness of the method.

2.5.2 Homoskedasticity

White’s Test (test-White)

• Econometrics : White Test with R, CrossValidated

mods_recs[[1]] cannot pass the White’s test, which means the variances of residuals do vary with different values of y.

mods_recs[[1]] %>% test_white(dat_recs, resi2 ~ x2 + I(x2^2), 2) %>% tab_ti()

whi	stat	df1	df2	p_value	prob	if_reject
White	5.587	2	298	0.0612	0.05	FALSE

2.5.3 Functional Form

RESET Test (test-RESET)

mods_recs[[1]] can pass RESET test.

mods_recs[[1]] %>% test_reset(dat_recs) %>% tab_ti()

#> Registered S3 methods overwritten by 'lme4':
#>   method                          from
#>   cooks.distance.influence.merMod car 
#>   influence.merMod                car 
#>   dfbeta.influence.merMod         car 
#>   dfbetas.influence.merMod        car

whi	stat	df1	df2	p_value	prob	if_reject
RESET	2.447	1	299	0.1178	0.05	FALSE

• Does lm() use partial correlation - R Squared Change, CrossValidated

References

Hendry, David F, and Bent Nielsen. 2007. Econometric Modeling: A Likelihood Approach. Princeton University Press.

Wood, Simon N. 2017. Generalized Additive Models: An Introduction with R. CRC press.