A Multilevel Nonlinear Profile Analysis Model for Dichotomous Data

Abstract

This study linked nonlinear profile analysis (NPA) of dichotomous responses with an existing family of item response theory models and generalized latent variable models (GLVM). The NPA method offers several benefits over previous internal profile analysis methods: (a) NPA is estimated with maximum likelihood in a GLVM framework rather than relying on the choice of different dissimilarity measures that produce different results, (b) item and person parameters are computed during the same estimation step with an appropriate distribution for dichotomous variables, (c) the model estimates profile coordinate standard errors, and (d) additional individual-level variables can be included to model relationships with the profile parameters. An application examined experimental differences in topographic map comprehension among 288 subjects. The model produced a measure of overall test performance or comprehension in addition to pattern variables that measured the correspondence between subject response profiles and an item difficulty profile and an item-discrimination profile. The findings suggested that subjects who used 3-dimensional maps tended to correctly answer more items in addition to correctly answering items that were more discriminating indicators of map comprehension. The NPA analysis was also compared with results from a multidimensional item response theory model.

Notes

¹Although this study employs random assignment, the proposed profile analysis technique is applicable to quasi-experimental or nonexperimental designs as well.

^aParameter values were fixed to zero.

**p < .01.

***p < .001.

²Specifically, the MIRT model estimated 36 item difficulties, 71 item discriminations for the two dimensions, and 4 experimental effects. Note that a discrimination parameter for the second dimension was fixed to one (Rijmen et al., 2003).

³It is important to note that the difference in sign is due to the fact that the first MIRT dimension and second NPA dimension were negatively correlated.