The nonrandom selection of don't knows in binary and ordinal responses: Corrections with the bivariate probit model with sample selection

On social surveys don't knows are a common answer to attitudinal questions, which often have binary or ordinal response categories. Don't knows can be nonrandomly selected according to certain demographic or socioeconomic characteristics of the respondent. To model the sample selection and correct for its bias, this paper discusses two types of bivariate models -binary-probit and the ordinal probit model with sample selection. The difference between parameter estimates and predicted probabilities from the analysis modelling the sample selection bias of don't knows and those from the analysis not modelling don't knows is emphasized. Two empirical examples using the 1989 General Social Survey data demonstrate the necessity to correct for the bias in the nonrandom selection of don't knows for binary and ordinal attitudinal response variables. A replication of the analyses using the 1990 and 1991 General Social Survey data helps demonstrate the reliability of the sample selection bias of don't knows.