The robustness of the bivariate ordinal probit model to the presence of response styles

Respondents may give di_erent answers to survey questions although they have the same underlying opinion. When data is collected among respondents with di_erent response styles, interpretations of models based on this data could be wrong. In this project we describe shortly the idea of response styles. We will study, in the case of two ordinal variables, the extent to which the bivariate ordinal probit model is a_ected by the presence of response styles. First we explain the model and derive the log-likelihood function, we then show how this log-likelihood function can be maximized. We will apply this model to empirical data. Furthermore, we will simulate ordinal data and scale a part of this data with response style curves. The parameter estimates of the models based on the partly scaled and non-scaled data are compared to measure the robustness of this model to the presence of response styles. When (dis)acquiescence is present, the correlation coe_cient is overestimated, the absolute value of the _ coe_cients decreases and the threshold values are shifted. This problem can be solved by adding a dummy-variable that indicates which respondents have this response style. The presence of midpoint responding and extreme responding leads to a change in the dispersion of the threshold values