Variance of the latent variable different than 1 in std.lv

[Rim Rj]

Hi everyone,

I am running a SEM with 3 latent variables (Habit, SDM and NSDM) aiming to study their influence on intentions (measured with one item Q5_1new). I decided to use as an estimation method WLSMV since I have ordered data. When looking to the results of my regression I noticed that the standardized variances of two of my latent variables are different than 1. Is this normal? What could be the reason behind this (In the unstandardized results I had the 1st item of each latent variable fixed to 1)?

My model specification is as follows:

SEMh1_1mod <- '
              #latent variables definition : Measurement model
              Habit =~ Q5_14 + Q5_15 + Q5_16 + Q5_17
              SDM =~ Q5_7 + Q5_8 + Q5_11 + Q5_12 + Q5_13
              NSDM =~ Q5_5 + Q5_6 + Q5_9 + Q5_10
             
              #regressions: structural model
              NSDM ~ a*Habit
              SDM ~ d*Habit
              Q5_1new ~ b*NSDM + c*Habit + e*SDM
             
              #covariances
              SDM ~~ NSDM
             
              #Indirect effect
              IE_NSDM := a * b
              IE_SDM := d * e
             
              #Total effect
              TE := c + (a * b) + (d * e) '

The part of the table of results where I have the problem:

Thank you in advance!

Rim.

[Terrence Jorgensen]

Variances are not model parameters, residual variances are. Residuals variances of exogenous variables are total variances, so the std.lv solution coincidentally shows the Habit variance as 1.  The endogenous variables have predictors, so when their total variance == 1, their residual variance == 1 - R^2 < 1.

Terrence D. Jorgensen

Assistant Professor, Methods and Statistics

Research Institute for Child Development and Education, the University of Amsterdam

http://www.uva.nl/profile/t.d.jorgensen

[Rim Rj]

Thank you Terrence for your answer! I understand better the results I am seeing.

Rim.