Message/Author 

JM posted on Tuesday, May 26, 2009  12:58 pm



Hi, when examining longitudinal measurement invariance, comparing equal form, factor loading, and indicator intercept models, I understand that chisq diff testing is done to check as to whether the nested models differ compared to the comparison model; however, should I also be looking at estimates in the output to check for specific changes or nonchanges in standardized or understandarized (not sure which) coefficients? Thanks! 


I would look at modification indices. 

Sean Tucker posted on Wednesday, August 26, 2009  8:46 pm



Dear Linda, I have a three wave longitudinal dataset with equal time intervals. Following Chan (1998) I am trying to test for measurement invariance but I can’t seem to find an applied example that shows the relevant MPlus syntax (including setting free vs. equal factor loadings, free vs. fixed error variances, etc) and guide to understanding the related output. Would you be so kind as to direct me to a simple applied example or provide the syntax in a reply? I’m relatively new to MPlus and I have a weak background in stats. Many thanks, Sean 


See the Topic 4 course handout starting with slide 77. 

Sean Tucker posted on Thursday, August 27, 2009  11:14 am



Many thanks, Linda. I received an error message (i.e., "*** ERROR in MODEL command Unknown variable(s) in a BY statement: (1) ") when running the model with factor loading invariance: V1 BY v11 v12 v13 v14 v15 v16 v17 (1)(6); V2 BY v21 v22 v23 v24 v25 v26 v27 (1)(6); V3 BY v31 v32 v33 v34 v35 v36 v37 (1)(6); Pages 532533 of the user manual describe the syntax for fixing parameter values. Would you be so kind has to describe what (1) – (6) means in expanded form. Should I be using different command for fixing the parameter values? Thank you for your help. Sean 


It should say (16). 

Sean Tucker posted on Thursday, August 27, 2009  1:21 pm



Thank you, Linda. Should I be concerned about this message? *** WARNING in MODEL command There are more equality labels given than there are parameters. Some equality labels will not be used. Equality: 16 When testing for partial intercept invariance some items do not appear in the commands on slide 90 (Topic 4). How do I determine which items are not subject to the equality constraint? Thank you, Sean 


Please send your output and license number to support@statmodel.com regarding the error message. Partial measurement invariance requires relaxing the equality constraints of some items which. Modification indices were used to determine which items. The Topic 1 course video covers testing for measurement invariance. You should listen to that and then the Topic 4 course video for a full explanation. 

Pamela May posted on Thursday, August 14, 2014  3:14 pm



Hello, I am testing measurement invariance for a latent difference model. I have the same construct, activity frequency, being tested at two time points. I am confused by the fact that I have the same degrees of freedom, for when I fix the factor loadings (chisquare = 27.30, df = 18), as well as when the factor loadings and the intercepts are fixed (chisquare = 350.02, df = 18). Would there be any reason that these two models have the same degrees of freedom? !Fixing factor loadings CA08 BY dv kv (1) lv (2) pv (3); CA12 BY Ev Mv (1) Nv (2) Rv (3); dv with Ev; kv with Mv; lv with Nv; pv with Rv; CA08 with CA12; !Fixing factor loadings and intercepts (same syntax as before plus this below) !Indicators are categorical, with five levels [dv$4 Ev$4] (4); [kv$4 Mv$4] (5); [lv$4 Nv$4] (6); [pv$4 Rv$4] (7); {dv@1 kv@1 lv@1 pv@1 Ev Mv Nv Rv}; Thank you, Pam 


If you have fixed scale factors at time 2 for the equal loading run, the equal loading+threshold run restricts 4 thresholds but frees 4 scale factors, so ends up with the same number of parameters. Now, in the second model you want to have the factor mean free at time 2. 

Pamela May posted on Thursday, August 14, 2014  3:42 pm



Thank you, Bengt, for your prompt and helpful reply! 


I am trying to run longitudinal measurement invariance analysis. The first part of the MODEL command is: MODEL: !TIME 1 INT3 BY y3int1* y3int2 y3int3 y3int4 y3int5 y33nt6 y3int7 (L1L7); EXT3 BY y3ext1* y3ext2 y3ext3 y3ext4 y3ext5 y3ext6 y3ext7 y3ext8 y3ext9 y3ext10 y3ext11 (L8L18); INT3  EXT3@1; !Time 2 INT5 BY y5int1* y5int2 y5int3 y5int4 y5int5 y5int6 y5int7 (L1L7); EXT5 BY y5ext1* y5ext2 y5ext3 y5ext4 y5ext5 y5ext6 y5ext7 y5ext8 y5ext9 y5ext10 y5ext11(L8L18); INT5EXT5@1; !TIME 3 INT9 BY y9int1* y9int2 y9int3 y9int4 y9int5 y9int6 y9int7 (L1L8); EXT9 BY y9ext1* y9ext2 y9ext3 y9ext4 y9ext5 y9ext6 y9ext7 y9ext8 y9ext9 y9ext10 y9ext11 (L8L18); INT9EXT9@1; I get the error message: *** ERROR in MODEL command There are more equality/parameter labels in the following statement than there are parameters. Problem found in the statement: EXT3 BY y3ext7 y3ext8 y3ext9 y3ext10 y3ext11 (L8L18) Are you able to advise on what I am doing wrong? Many thanks 


!TIME 3 INT9 BY y9int1* y9int2 y9int3 y9int4 y9int5 y9int6 y9int7 (L1L8); The above statement has 8 labels and 7 factor indicators. 


OK many thanks, i have corrected that mistake. However I still get error messages with the following code: cbcl3 BY y3int1* y3int2 y3int3 y3int4 y3int5 y3int6 y3int7 y3ext1 y3ext2 y3ext3 y3ext4 y3ext5 y3ext6 y3ext7 y3ext8 y3ext9 y3ext10 y3ext11(L1L18); ERROR in MODEL command There are more equality/parameter labels in the following statement than there are parameters. Problem found in the statement: cbcl3 BY y3ext3 y3ext4 y3ext5 y3ext6 y3ext7 y3ext8 y3ext9 y3ext10 y3ext11 (L1L18). As I have 18 variables I don't know why this is happening. Could you help me identify where I have gone wrong? Many thanks 


Please send the full output and your license number to support@statmodel.com. 

Kurt Beron posted on Tuesday, September 08, 2015  10:46 am



Hi Drs. Muthen, I am trying to check for longitudinal measurement invariance of constructs over a number of time periods. The observed indicators of the constructs, though, are a combination of counttype variables (Poisson or negative binomial and, perhaps, inflated). I understand the steps for the series of constraints necessary to go from least restrictive to most restrictive with continuous or categorical data but have not found the restrictions for, say, a (zeroinflated) negative binomial or the Poisson versions. Can you suggest an approach in Mplus for this, or direct me to where this might be documented? Thanks. Kurt 


I haven't seen this discussed, but I would simply hold all the parameters invariant: intercept, slope, dispersion, inflation. Although I guess strictly dispersion wouldn't have to be invariant since it only influence the variance, not the mean. I don't think one can view it like for continuous outcomes where invariance for loadings only makes the SEM part comparable. 


Dear Drs Muthen, I am currently testing longitudinal measurement invariance and my results are suggesting that scalar invariance is not met. I have read of the alignment and alignmentwithincfa methods in Asparouhov & Muthen (2014) and Marsh, Guo, Parker, Nagengast, Asparouhov, Muthen, and Dicke (2016, accepted) for dealing with this challenge when considering measurement noninvariance between groups, but understand that these procedures are not possible when considering longitudinal measurement invariance. Therefore, is it still considered acceptable to seek partial intercept invariance using modification indices to identify the variable(s) to be freely estimated in longitudinal models (cf. Byrne, Shavelson, & Muthen, 1989)? If not, please could you kindly point me in the direction of a more appropriate, alternative approach? Many thanks, Daniel 


Partial intercept invariance is probably the way to go. 


Okay great, thanks Bengt. Regards, Dan 

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