When analysing binary outcomes, logistic regression is the analyst’s default approach for regression modelling. The logit link used in logistic regression is the so called canonical link function for the binomial distribution. Estimates from logistic regression are odds ratios, which measure how each predictor is estimated to increase the odds of a positive outcome, holding the other predictors constant. However, most people find risk ratios easier to interpret than odds ratios. In randomized studies it is of course easy to estimate the risk ratio comparing the two treatment (intervention) groups. With observational data, where the exposure or treatment is not randomly allocated, estimating the risk ratio for the effect of the treatment is somewhat trickier.
Banning p-values from journals
A psychology journal (Basic and Applied Social Psychology) has recently caused a bit of stir by banning p-values from their published articles. For what it’s worth, here’s a few views on the journal’s new policy, and on the use of p-values and confidence intervals in empirical research.
Interval regression with heteroskedastic errors
Interval regression allows one to fit a linear model of an outcome on covariates when the outcome is subject to censoring. In Stata an interval regression can be fitted using the intreg command. Each outcome value is either observed exactly, is interval censored (we know it lies in a certain range), left censored (we only know the outcome is less than some value), or right censored (we only know the outcome is greater than some value). In Stata’s implementation the robust option is available, which with regular linear regression can be used when the residual variance is not constant. Using robust option doesn’t change the parameter estimates, but the standard errors (SEs) are calculated using the sandwich variance estimator. In this post I’ll briefly look at the rationale for using robust with interval regression, and highlight the fact that if the residual variances are not constant, unlike for regular linear regression, the interval regression estimates are biased.