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Dear Dr. Muthèn: I have to compute a latent variable (ABS – affective balance score) that represents the latent difference of two latent variables (PA – positive affect and NA negative affect). Then I need to regress the obtained latent score (ABS) on another latent variable (IQ). I have heard of computing latent difference score which should be NA = PA@1 and then computing NA on IQ – where NA represents now the ABS. Is that syntax correct? OR do you have other suggestions how to best compute the difference of two latent variables? Thank you MODEL: IQ by IQ_VB IQ_RA IQ_VI IQ_SP; NA by Q_NA_1_2 Q_NA_2_2 Q_NA_3_2; PA by Q_PA_1_2 Q_PA_2_2 Q_PA_3_2; NA on PA@1; NA on IQ; 


Remove: NA on PA@1; NA on IQ; Try: diff BY; diff ON pa@1 na@1; diff@0; 

Jiawen Chen posted on Tuesday, August 26, 2014  4:04 pm



Dear Dr. Muthèn: I wonder if I can model the latent difference score of two different variables because so far all I have come across is about modeling latent difference score of the same variable across different waves. I have a variable called intrinsic work values, measured by three items: "if you are to look for a fulltime job, how important are the following job characteristics (5 point scale): a)job is interesting; b)I make most of the decisions; c)I feel accomplished." I have another variable called intrinsic work rewards, measured by exactly the same items, only the question was asked differently, "describe how strongly you agree with the following characteristics about your current job (5 point scale)." So if I want to study how the discrepancy between work values and rewards predicts a host of outcome variables, is it appropriate to model the latent difference score between them at the same wave? Can I also do a thirdorder latent growth model of the latent difference score across multiple waves? Or some other method may be more suitable for what I want to study? Thank you very much! 


It seems to me that one can do some version of latent difference modeling also with different variables, but I haven't tried. 

Lixin Jiang posted on Wednesday, September 03, 2014  9:07 pm



I have two time points measures (NSsad, SSsad), which have been counterbalanced in my study. Now I want to use gender and personality trait to predict this latent change. See below that I have used it as latent growth model. However, it seems to be misleading as it is not growth itself. How do I model this "latent difference/change score model"? Thanks. i sNSsad@0 SSsad@1; s on sex CA; NFSAD(1); SFSAD(1); 


A linear growth model cannot be identified with only two time points. I would instead create a change score as follows: f BY nssad@1 sssad@1; f ON sex ca; 

Roger Brown posted on Thursday, September 04, 2014  9:39 am



I worked up this simple difference test with a covariate the other day and checked it against a group test on a difference vector. Is this what you are thinking of? title: LCS used to estimate paried ttest with covariate data: file is ttest.txt; variable: names are x y1 y2; model: lcs on y1@0; lcs by y2@1; y2 on lcs@1; y2 on y1@1; y2@0; lcs on x; 


Shouldn't there be a negative sign somewhere? 

Lixin Jiang posted on Thursday, September 04, 2014  4:21 pm



Thank you, Roger. The results based on your codes were more consistent with the regression results from SPSS. 

Meike Slagt posted on Thursday, November 13, 2014  9:43 am



Dear Dr. Muthen, I'm trying to estimate latent change scores, using ordinal data. I can get one part of that model to work (the measurement part), I can get the other part of that model to work (the difference scores, using factor scores saved from the measurement part as input for the difference scores), but I can't get the complete model to converge. That is, I get parameter estimates, but no standard errors. I'm providing the Mplus code I used in the next post, because it doesn't fit in this post anymore. I would really appreciate advice on this: Why is my model not converging; Is my sample size just to small for this (N=190); Am I forgetting certain parameter constraints leading my model to be unidentified? Thank you so much in advance! 

Meike Slagt posted on Thursday, November 13, 2014  9:47 am



!Measurement Part, factorial invariance across time neg1 BY PreN_Boos PreN_Ver PreN_Bang (13); neg2 BY PostN_Boos PostN_Ver PostN_Bang (13); [PreN_Boos$1 PostN_Boos$1] (4); [PreN_Boos$2 PostN_Boos$2] (5); [PreN_Ver$1 PostN_Ver$1] (6); [PreN_Ver$2 PostN_Ver$2] (7); [PreN_Bang$1 PostN_Bang$1] (8); [PreN_Bang$2 PostN_Bang$2] (9); {PreN_Boos@1 PreN_Ver@1 PreN_Bang@1}; !Difference scores !Works when I save factor scores of neg1 and neg2 and use those as input. Doesn’t work when I try to estimate measurement part and difference scores in one model. Dif_Neg BY neg2@1; !define latent change by T2 neg2 ON neg1@1; !autoregression T2 T1 neg2@0 neg1; !var at T2=0, estimate var T1 & change [neg2@0 Dif_Neg neg1]; !mean at T2=0, estimate mean T1 & change Dif_Neg ON neg1; !intercept change association This model results in a warning: THE MODEL ESTIMATION TERMINATED NORMALLY THE STANDARD ERRORS OF THE MODEL PARAMETER ESTIMATES COULD NOT BE COMPUTED. THE MODEL MAY NOT BE IDENTIFIED. CHECK YOUR MODEL. PROBLEM INVOLVING THE FOLLOWING PARAMETER: Parameter 10, [ DIF_NEG ] THE CONDITION NUMBER IS 0.147D16. 


We discourage postings in several windows. For a longer question like this, please send your problematic outputs, data, and license number to Support@statmodel.com. 


Hi, Mplus team, I need to model a difference/change in the factor scores between the baseline model T and the model at T2. Both models are based on the same set of respondents. The goal is to estimate the change and save the corresponding score to further use in the regression analysis. I wonder whether you could comment on the following approach or, perhaps, point me at the better alternatives. My intuition was to test for the invariance in two measurement models to ensure the scales have identical metric at T and T2, save the factor scores and compute the difference. This being said, I am not sure whether this approach would be perfectly appropriate. I think I stumbled upon Linda's answer somewhere on the forum that invariance should not be tested on the same sample of respondents. I'd appreciate any suggestions. For what it's worth, the model to be estimated is hierarchical CFA, in which several constructs load on a general construct. 


Analyze a model for the 2 time points jointly. Check scalar measurement invariance. Fix the factor mean(s) at zero for the first time point and let them be free to be estimated for the second time point. No need for factor scores. The factor mean(s) at the second time point represent(s) the difference from the first time point. 


Excellent! Thank you so much for the prompt reply. 


Hi Mplus team, I am new to Mplus, so please excuse my basic question. I would like to calculate latent difference scores for two latent constructs in the following model: y = (ab) + (cd) with a = construct with the indicators a1,a2,a3, b with b1,b2,b3, c with c1,c2,c3, and d with d1,d2,d3. How can I translate this to a mplus model? Thank you! 

IW posted on Monday, June 15, 2015  12:20 pm



Hello Dr. Muthen, Can you explain your previous answer a bit more or perhaps point me to a resource that goes into depth(re: Monday, March 16, 2015  4:03 pm)? McArdle (2009) seem to be suggesting a different approach. McArdle, J. J. (2009). Latent variable modeling of differences and changes with longitudinal data. Annual review of psychology, 60, 577605. 


Time points are analogous to groups in that scalar measurement invariance makes it possible to identify a factor mean difference. That was my reply. I don't know about specific references. With 2 time points there is not much else one can do. 

Sara Geven posted on Monday, September 07, 2015  10:32 am



Dear Prof Muthen, I would like to analyze a change in a factor measured at two time points. However, I would also like to incorporate the effect of the factor score at wave 1 on the change in factor scores. This is not possible when I use the code described above (as the path from delin1 to diff is constrained): diff BY; diff ON delin1@1 delin2@1; diff@0; I was wondering whether there is a way to do this in Mplus. I know it is possible when the difference score is a latent variable (in line with MCardle's (2009) paper that is also mentioned above): delin2 ON delin1@1; delin1 delin2@; [delin1 delin2@0]; delta_b BY delin2@1; delta_b; [delta_b]; However, somehow this model seems to be unidentified when I use factors to construct delin1 and delin2 (instead of scales). Do you know what might be going on? Or do you know another way to analyze this? Thank you in advance Sara Geven 


Dear Professor Muthen, I am hoping to use latent difference score modeling to examine changes in two processes, however variables at each time point are theoretically and empirically binomial. Do you know of a resource for latent difference score modeling with binomial variables? Thank you. Sincerely, Lance Rappaport 


Sarah, please send your output, data, and license number to support. 


Lance  you may want to ask this on SEMNET. 

Sara Geven posted on Wednesday, September 09, 2015  1:19 pm



Dear Bengt, Thank you for your willingness to help. I just solved the problem. One item intercept had to be fixed for identification. Sara 

Seth Frndak posted on Friday, December 18, 2015  8:18 am



I am attempting to create a LDS model with 4 timepoints. The first three timepoints 13 are 1year apart. The 4th timepoint is 4 years after the 3rd timepoint. So you could explain it as timepoints 13 & 7. I know that one assumption of the LDS model is that the autoregressive paths are constrained to 1. If an autoregressive path is modeled between 3 and 7, is there a way to estimate the longer time gap without violating model assumptions? Furthermore, would additional parameterization be necessary to estimate the time 7 difference score after taking the adjusted autoregressive path into account? 


You may want to ask that question on SEMNET. 

Seth Frndak posted on Friday, February 19, 2016  8:08 am



What are the implications of skewed data in a latent difference score framework? It seems (Burt and Obradovic 2012) that skewness of the baseline scores can create spurious relationships with covariates. I have been unable to find any resources on LDS and highly skewed data. Can you point me in the right direction? 


Don't know  try SEMNET. 

Mark Prince posted on Friday, February 26, 2016  9:31 am



Hi there, I am attempting to run a monte carlo simulation for a bivariate latent change score model and am getting the error: *** FATAL ERROR THE POPULATION COVARIANCE MATRIX THAT YOU GAVE AS INPUT IS NOT POSITIVE DEFINITE AS IT SHOULD BE. My syntax works with real data (using code I got from a workshop with Jack McArdle). I am using the parameter estimates from that output in the simulation to look at power, but I get the error above when I do that. Do you have any suggestions? 


Send output to Support along with your license number. 


Drs. Muthen, I was wondering if it would be possible to run a latent difference score (LDS) model in MPlus with individuallyvarying times for each of the latent variables. Also, the time points are not necessarily consecutive since an individual can have data at up to four time points (covering a span of roughly four years) and in that case, I would use only the earliest and latest time points for the LDS. I'm using one construct at two different time points for the LDS with covariates and a distal outcome. If you could point me to suitable references/MPlus code for a LDS model with individuallyvarying times, I would really appreciate it. Thanks for your help. Thanks, Raghav 


I don't have such a script  try SEMNET. And if you find it, please post it. 

SM posted on Tuesday, April 19, 2016  5:13 am



Hi, I am trying to calculate the latent difference between informants, on the same variable, which difference I then want to predict. I tried two different ways. First the way Linda wrote on April 23, 2012: diff BY; diff ON f1@1 f2@1; diff@0; In this case the mean of the Diff does not appear on "Model Results" but only on "Sample Statistics for Estimated Factor Scores". Second, I tried: [f1] (a); [f2] (b); diff BY; diff BY f1@1 f2@1; [diff] (c); Model Constraint: c = ab; In the latter case, the Mean of the Diff appears in the model results. Although the estimate of the mean Diff is almost identical in both methods (they differ by 0,001 unstandardized), the SE's are totally different (0,246 and 0,027 respectively). According to the first method, mean Diff is not significant. Furthermore, comparing "a" and "b" by means of Wald test also results in significant difference. How do you explain this difference in methods? Since I would like to predict the Diff, how should I proceed? Thank you. 

Joe posted on Thursday, July 28, 2016  12:32 pm



Can I run a latent change score model if both variables have a Poisson distribution? that is, something like the following? VARIABLE: COUNT IS t1 t2; Model: f BY t1@1 t2@1; 


Poisson modeling considers the log mean for the count variable. I therefore don't think a linear model of the difference makes sense. 

Seth Frndak posted on Monday, August 01, 2016  12:17 pm



There seems to have been some work in a twopart modeling framework with latent change scores. This is with zeroinflated data, however. See: http://www.tandfonline.com/doi/abs/10.1080/00273171.2016.1144501 


Good. 

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