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