Defining Models

Introduction

The MODEL keyword is most important, because it defines, well, your model. Simple models are set up very easily. To these we will turn now.

Typically, you will have a part in your model where you will relate observed indicators to latent variables. Another part will then relate the latent variables to each other.

Let's assume that we have measured 14 indicators, named v1 to v14 on the VARIABLES statement; these are supposed to be related to four latent variables. Mplus is informed about these relationships by the first four statements following the MODEL command that use BY to connect the latent variables to their indicators (the names for the latent variables can be chosen arbitrarily, of course in line with the restrictions for all variable names). The relationships among the latent variables, or factors, are defined by the next two lines, with latent variables related to each other by ON. Here, f3 is regressed on f1 and f2; f4 is regressed on f3 only.

MODEL:
      f1 BY v1-v4;
      f2 BY v5-v7;
      f3 BY v8-v12;
      f4 BY v13 v14;
      f3 ON f1 f2;
      f4 ON f3;

Note that a number of additional elements for indicating models exist that are needed for more complicated models like multilevel or growth curve models, latent class analysis and the like.

Constraints on parameters

Tests of equality of parameters

In most instances, constraints are set on parameters in order to test the hypothesis that two (or perhaps more) parameters do not differ significantly from each other. There is a very easy way to treat this simple case.

For simplicity's sake, let's suppose that we have a linear regression model with a few independent variables, such as in:

MODEL:
f1 on f2-f5;

If, for instance, you wish to test that the coefficients of f2 and f3 are equal, you will write the following;

MODEL:
      f1 ON f4 f5;
      f1 ON f2 (1);
      f1 ON f3 (1);

This will indicate that equality of f2 and f3 is the first (in this case: the only) constraint to be implemented. Note that f2 and f3 now are missing from the first line. Now, if you might also wish to test that the coeffients of f4 and f5 are equal to each other (but not to those of f2 and f3), you will deal with these in same way, only with the number 2 in parentheses. In contrast, if you wish to test that the coefficient of f4 is equal to that of f2 and f3 (but that of f5 may be different), you will add f1 ON f4 (1); to the lines above, with only f5 remaining in the first line.

Other constraints

Other constraints can be implemented with the command MODEL CONSTRAINT.