## 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 . True LR tests are not possible with svyglm() objects since they were not fit using maximum likelihood . 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) 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
regTermTest(fit.ex8.1,
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

### References

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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.