IRT models are often referred to as latent trait models, especially in the field of sociology. The term latent trait is used to emphasize that observed discrete responses are manifestations of hypothesized traits, constructs, or attributes that cannot be directly observed. For that reason, IRT models belong to the more general modeling framework called latent variable models. Other models that belong to the latent variable model framework include factor analysis models, finite mixture models, and mixed effect models. The relationships between these different latent variable models can be described as shown in Table 51.2.

Table 51.2: Latent Variable Models

Latent Variable |
|||
---|---|---|---|

Continuous |
Discrete |
||

Observed Variable |
Continuous |
Factor analysis |
Finite mixture model |

Discrete |
Item response theory |
Latent class analysis |

This table suggests that latent variable models can be classified into four groups, based on the measurement scale of observed and latent variables. These different latent variable models can be fitted by different SAS procedures: PROC FACTOR for factor analysis models, PROC FMM for finite mixture models, and PROC IRT for item response theory models. IRT models are more closely related to factor analysis models. They can be considered a version of factor analysis models of discrete rather than continuous responses.