The short answer
None of the variables in a regression or path model (i.e., when all variables are manifest/observed), none of the parameters are constrained to equality by default.
An example with explanation
Below is a simple two-group path model with an observed variable y regressed on three other observed variables, x1, x2, and x3.
Data:
File is D:\data\mydata.dat ;
Variable:
Names are female x3 x1 y x2;
Missing are all (-9999) ;
grouping is female (0 = male 1 = female);
Analysis:
Type = general ;
Model:
y on x1 x2 x3;
We have omitted most of the Mplus output file. To download the entire file click here. Below is the MODEL RESULTS section for males and females (the output for males appears first, followed by the output for females). Comparing the regression coefficients (denoted ON), the intercept and the residual variances, we see that none of these coefficients are constrained to equality by default.
MODEL RESULTS
Two-Tailed
Estimate S.E. Est./S.E. P-Value
Group MALE
Y ON
X1 0.352 0.105 3.365 0.001
X2 0.050 0.089 0.560 0.575
X3 0.450 0.105 4.307 0.000
Intercepts
Y 8.205 4.798 1.710 0.087
Residual Variances
Y 55.518 8.231 6.745 0.000
Group FEMALE
Y ON
X1 0.453 0.102 4.455 0.000
X2 0.046 0.084 0.546 0.585
X3 0.211 0.098 2.161 0.031
Intercepts
Y 13.632 3.958 3.444 0.001
Residual Variances
Y 43.290 5.864 7.382 0.000