Investigating Response Profiles Using a Constrained Mixture Rating Scale Model

• In Event: Using Mixed Models to Investigate Tendency, Process, and Typology in Item Responding

Abstract

1. Objectives or purposes

The purpose of the study is to investigate the success of a new methodology for identifying different sub-populations of respondents in surveys using a finite mixture approach based on polytomous Rasch modeling. The proposed model aims to identify sets of respondent profiles that differ in their response tendencies. For instance, the model could be used to discover latent classes consisting of respondents either avoiding or preferring extreme categories.

2. Perspective(s) or theoretical framework

Using a Rasch mixture model (Rost, 1990), one can identify latent classes which have class-specific item parameters (item difficulties). However, polytomous data (e.g., a Likert scale) require polytomous variants of such models that allow a class-specific set of step (threshold) parameters as in Andrich (1978).

3. Methods, techniques, or modes of inquiry

In the polytomous Rasch mixture model (Rost, 1990), each threshold parameter is modeled to have a class-specific difficulty. Rost and von Davier (1995) proposed the rating scale restriction. We.extend this approach to polytomous contexts.
However, this comparison might result in ambiguity, as a combination of item and step parameters from two different latent classes can result in similar parameters, even though the respective item and step parameters might be substantially different between the classes.
To deal with this problem, we use two techniques:
1 We fix item locations between latent classes and investigate the difference in threshold parameters between the classes (still using the rating scale formulation, namely having a single set of step parameters for all items).
2. Alternatively, we can also identify a rating-scale mixture model in which the threshold parameters are fixed between classes while item locations are allowed to differ in difficulty across classes.

4. Data sources, evidence, objects, or materials

The first part of the analysis includes a set of simulated datasets under various conditions. These conditions vary by the number of latent classes, population size, number of items and number of ordinal categories of items. For the second part, we present findings from analyses of three real-life datasets from Likert-type surveys and show how these findings can be used to get new insights from the data.

5. Results and/or substantiated conclusions or warrants for arguments/point of view

Detailed results for these analyses cannot be displayed in this brief abstract, however Figures 1- 3 are a very graphic illustration of the power of the technique. These each show the pattern of item characteristic curves generated by the estimated set of step parameters for three latent classes in a single data set. Class 1 is the “regular” class, while Class 2 is the class of respondents who tend to avoid extremes, and Class 3 is the class that prefers extremes.

6. Scientific or scholarly significance of the study or work

This work is aiming to contribute to the investigation of the typologies of response behaviors. Methodology and findings from this work can be extended to allow person-level covariates in order to allow investigating relationship of discovered latent profiles with these variables.

Authors

• Perman Gochyyev, University of California - Berkeley

• Mark R. Wilson, University of California - Berkeley