Course Text: Pages 14-15
In traditional LC models, the latent classes account for all associations between the response variables/ indicators. That is, for cases in the same latent class, the indicators are statistically independent. In some cases, this ‘local independence’ property is not desired. In such cases, one or more direct effect parameters can be included in a model to account for certain bivariate associations outside the LC portion of the model.
For example, suppose that 6 items are used to identify a dichotomous scale (say, depressed vs non- depressed), and that very similar wording is used for 2 of the 6 indicators creating additional (extraneous) association between these 2 items. Since this additional association is not related to the latent variable depression, it should be accounted for outside the LC portion of the model using a direct effect, so that the latent classes will be defined based only on the common association shared by all 6 indicators.
An example of direct effects with continuous indicators is given in Exercise #L1, where it is desired that the latent classes represent different types of diabetes – persons with Chemical diabetes, those with Overt diabetes, and cases known to have neither of these types of diabetes (‘Normal’ individuals). In this example, we will see that a correlation between two of the indicators is not relevant to distinguishing between these 3 latent classes. As such, a direct effect is included in the final model to account for this extraneous association.
Direct effects can also occur between covariates and indicators, a topic that is related to item bias or differential item functioning. For example, suppose the wording in one or more indicators in a 10-indicator scale tends to elicit different responses between males and females regardless of their latent class. This is an indication of the existence of gender bias in the item(s). Such item bias is also known as Differential Item Functioning (DIF) since the item functions differently for females than for males.
To account for DIF and remove the effects of such item bias it is necessary to not only include Gender as an active covariate in the model, but also include a direct effect between Gender and the item(s) affected by DIF. For further discussion of this issue, see Structural Equation Modeling (Vermunt and Magidson, 2020), and the example provided there, which is the subject of Exercise K.
Assigned Reading:
K1: Local Dependencies, Section 3.4 (page 108)
K2: Diabetes Example (pages 8-9)
K3: Structural Equation Modeling (Vermunt and Magidson, 2020)