8.8 Likelihood ratio test vs. Wald test

As we did in previous chapters, we used Wald tests for p-values in this Chapter. However, likelihood ratio (LR) tests may perform better (Thomas and Rao 1987). True LR tests are not possible with svyglm() objects since they were not fit using maximum likelihood (Lumley 2010). However, the function regTermTest() can be used to carry out a “working” LR test for weighted linear, logistic, or Cox regression models (the Rao-Scott LR test) (Rao and Scott 1984; Lumley and Scott 2013, 2014) to compare any two nested models, similar to anova() which we used in previous chapters.

regTermTest() can therefore obtain an overall Type 3 Wald or LR test for a categorical predictor with more than two levels. To get a test for a single level of a categorical predictor, first create indicator variables for the levels of that predictor as described in Section 6.18.

Example 8.1 (continued): Use a LR test to test the overall significance of race/ethnicity in the weighted adjusted linear regression model for fasting glucose.

# Model fit previously
fit.ex8.1 <- svyglm(LBDGLUSI ~ BMXWAIST + smoker + RIDAGEYR +
                      RIAGENDR + race_eth + income,
                 family=gaussian(), design=design.FST.nomiss)
# LR test for race_eth
            test.terms = ~ race_eth,
            df = degf(fit.ex8.1$survey.design),
            method = "LRT")
## Working (Rao-Scott+F) LRT for race_eth
##  in svyglm(formula = LBDGLUSI ~ BMXWAIST + smoker + RIDAGEYR + RIAGENDR + 
##     race_eth + income, design = design.FST.nomiss, family = gaussian())
## Working 2logLR =  11.29 p= 0.042 
## (scale factors:  1.8 0.93 0.31 );  denominator df= 15


———. 2010. Complex Surveys: A Guide to Analysis Using r: A Guide to Analysis Using r. John Wiley; Sons.
Lumley, Thomas, and Alastair Scott. 2013. “Partial Likelihood Ratio Tests for the Cox Model Under Complex Sampling.” Statistics in Medicine 32 (1): 110–23. https://doi.org/10.1002/sim.5492.
———. 2014. “Tests for Regression Models Fitted to Survey Data.” Australian & New Zealand Journal of Statistics 56 (1): 1–14. https://doi.org/10.1111/anzs.12065.
Rao, J. N. K., and A. J. Scott. 1984. “On Chi-Squared Tests for Multiway Contingency Tables with Cell Proportions Estimated from Survey Data.” The Annals of Statistics 12 (1): 46–60. https://www.jstor.org/stable/2241033.
Thomas, D. Roland, and J. N. K. Rao. 1987. “Small-Sample Comparisons of Level and Power for Simple Goodness-of-Fit Statistics Under Cluster Sampling.” Journal of the American Statistical Association 82 (398): 630–36. https://doi.org/10.1080/01621459.1987.10478476.