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Size and power of tests for dependency in regressions with ordinal variables
Keywords
size and power tests, polychoric correlation tests, canonical correlations tests, regressions with ordinal variables, Monte Carlo simulation
Abstract
In political science which factors that influence citizens' faith and trust in government, i.e. Political Efficacy, is of great importance. The statistical analysis is often based ordinal variables collected using surveys. In this paper we perform an interesting Monte Carlo simulation investigating the size and size adjusted power properties of ten tests for the dependency of one ordinal variable on one continuous, one binary and one ordinal variable. Tests include regression models, logit and probit where the exogenous variable is coded as a Likert scale variable or where dummies are used, test based on polychoric correlation and tests based on canonical correlation. Overall the test based on polychoric correlation performs best but is beaten in certain circumstances by the canonical correlation test. But the canonical correlation test performs really bad in some cases while the polychoric correlation test does not have a bad performance in any situation. Interestingly, the motivating example of analyzing Political Efficacy shows very similar results as the Monte Carlo simulation.