I have several binary variables ( at two-time points year 1 and 2 (say, Y1_yr1, Y1_yr2, Y2_yr1, Y2_yr2, Y3_yr1, Y3_yr2, Y4_yr1 and Y4_yr2) and a few covariates (e.g. X1, X2, X3).
I have made the Y variables ordered (to get DWLS) and ran the following codes in lavaan.
mod <- '
# Year 1
Y1_yr1 ~ Y3_yr1 + X1 + X2 + X3
Y2_yr1 ~ Y3_yr1 + X1 + X2 + X3
Y3_yr1 ~ Y1_yr1 + Y2_yr1 + X1 + X2 + X3
Y4_yr1 ~ Y1_yr1 + Y2_yr1 + Y3_yr1 + X1 + X2 + X3
# Year 2
Y1_yr2 ~ Y3_yr2 + Y1_yr1 + X1 + X2 + X3
Y2_yr2 ~ Y3_yr2 + Y2_yr1 + X1 + X2 + X3
Y3_yr2 ~ Y1_yr2 + Y2_yr2 + Y3_yr1 + X1 + X2 + X3
Y4_yr2 ~ Y1_yr2 + Y2_yr2 + Y3_yr2 + Y4_yr1 + X1 + X2 + X3
fit <- sem(mod, data=dat)
The model converges normally but I find some confusing results:
1) The path Y2_yr1 -> Y3_yr1 is positive and significant. But the path Y3_yr1 -> Y2_yr1 is negative and significant. In individual logistic regressions, both associations were positive and significant. I expected both paths to be positive and significant in SEM too. Why does it happen and am I making any mistake? Is the testing of the bidirectional relationship meaningful here given the information I have? Our intuition was that some people having a presence of Y3 (depression) will be more likely to show the presence of Y2 (addiction) and again some people having a presence of Y2 (addiction) will be more likely show a presence of Y3 (depression).
2) The beta coefficient is >1 for the path Y2_yr1 -> Y2_yr2. Can it be greater than 1 as both variables are binary? How should I interpret this?