# test for trend in ordinal response variable

I have an ordinal response variable and multiple explanatory variables-both continuous and categorical. What I'd like to do is check for any univariate trend between the the different explanatory variables and the response variable. is it reasonable to just use a logistic ordinal model for each explanatory variable as long as the proportional odds assumption is fulfilled?

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That is not unreasonable. One always has to consider whether univariable (unadjusted) analyses are informative. For univariable analysis it is fine to just use a rank correlation coefficient. One of the most pertinent ones for this situation, when $X$ is continuous or binary, is Somers' $D_{xy}$, which does not penalize for ties on $Y$. You can also use Spearman's $\rho^2$ which also handles the case when $X$ is categorical by considering multiple dummy variables and computing the ordinary $R^2$ against $rank(Y)$ to obtain a scaled version of the Kruskal-Wallis test. The R Hmisc package spearman2 function makes these easy to calculate and chart using a dot plot.
Don't know about tetrachoric correlation but the only reason I sometimes square $\rho$ is so I can handle the Kruskal-Wallis situation of multiple groups. $\rho^{2} = R^{2}$ where $R^2$ is the ordinary multiple $R^2$ for all the dummy variables against $rank(Y)$. If all predictors had only one degree of freedom and I keep assuming monotonicity I'd use $\rho$. – Frank Harrell Jun 9 '14 at 13:31