Ordinal Regression Analysis in Educational Research

• In Event: 46.063 - Multiple Regression: Principles and Practices

Abstract

In practice, observations are often analyzed using data sets containing ordinal rather than continuous variables. At times researchers may treat ordinal data as though it has the properties of continuous data, despite the required adherence of given assumptions dependent on the nature of the data. This could be detrimental as it may result in inaccurate interpretation of results. This presentation will provide an example of ordinal regression analysis, demonstrating its value as a powerful tool when considering the correlation or predictive value of ordinal variables.

The example will investigate whether verbal and quantitative GRE scores are significant predictors of socioeconomic status using ordinal regression analysis with SPSS statistical software. This presentation will outline the required steps to perform this analysis, and will highlight the importance of the link function when considering the nature of the given data.

The use of each link function and differences in the resulting output will be reviewed, demonstrating the danger of misinterpreting results due to a failure to consider the properties of ordinal data. For instance, when using the default logit link function, results of the above research question reflects conflicting output of perfect prediction based on non-significant variables. This occurs because the logit link function assumes evenly distributed categories in the data. In contrast, acknowledgment of the normal distribution of the socioeconomic status data necessitates the choice of the probit link function. Analysis conducted using this function reveals that the variables are in fact significant predictors.

Additional link functions and their uses in practice will be explored, such as the use of the negative log-log link function used when lower categories are more probable, and the complementary log-log for use when higher categories are more probable. The aim of these examples will be to provide a better understanding of ordinal regression techniques, providing useful tools in practice that will assist in presenting correct analysis of ordinal data, therefore more effective interpretations of results.

Author

• Erin O'Connor, University of Alabama