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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. 


Dear Drs. Muthen, I am trying to conduct a bivariate latent difference score analysis, and I have two variables estimated at only two time points. I tried to adjust a syntax I found that refer to several time points, but I think I am doing something wrong. I get the message that "THE DEGREES OF FREEDOM FOR THIS MODEL ARE NEGATIVE. THE MODEL IS NOT IDENTIFIED". I attach the syntax. I would appreciate your help in understanding my mistake: (chy and chx are the latent change variables). y2 on y1; chy by y2; x2 on x1; chx by x2; chy on y1; chy on x1; chx on x1; chx on y1; Thank you 


You want to ask this question on SEMNET. 


Dear Drs. Muthén, I have two wave data and would like to examine the effect of sleep on change in various cardiometabolic parameters. First of all, I fitted a model to obtain the latent change in waist circumference: z_wst_T3 on z_wst_T1@1; z_wst_T1 z_wst_T3@; [z_wst_T1 z_wst_T3@0]; dewst BY z_wst_T3@1; dewst; [dewst]; I get a warning that the latent variable covariance matrix is not positive definite and see that the variance of my delta (dewst) is significantly negative. Is there any solution to this problem? I used the same code for blood pressure and this worked fine. Best, Barbara 


SEMNET will be a good outlet to help you with this. 


I am trying to estimate a random slope for the effect of a latent difference score on the slope of a multilevel latent growth model. However, it seems that thiis not possible as I get fatal error messages. Here's my syntax for the within part. What am I doing wrong? MODEL: %WITHIN% CHperprb by peerprb3@1; peerprb3 on peerprb@1; peerprb3@0; CHperprb with peerprb; [CHperprb peerprb peerprb3@0]; CHperprb peerprb; iw sw  homo@2 homo2@1 homo3@0; s1  sw ON CHperprb; 


We need to see the fatal error message  send your output to Support along with your license number. 


Maybe I should be more precise. The error message I received was: THE ESTIMATED WITHIN COVARIANCE MATRIX COULD NOT BE INVERTED. COMPUTATION COULD NOT BE COMPLETED IN ITERATION 1. CHANGE YOUR MODEL AND/OR STARTING VALUES. THE MODEL ESTIMATION DID NOT TERMINATE NORMALLY DUE TO AN ERROR IN THE COMPUTATION. CHANGE YOUR MODEL AND/OR STARTING VALUES. I am assuming this has to do with the fact that I am trying to estimate a random slope for an effect of a latent variable (CHperprb) on another latent variable (slope). So I would like to know whether this is in theory possible. If it is, then it may have to do with my particular data and I am willing to send it to support. 


Dear all, I am trying to estimate McArdles Latent Difference Score model on two levels using the following code. %within% diffa BY; t2_att ON t1_att@1 diffa@1 ; t2_att@0; t1_att WITH diffa; %between% diffa_b BY; t2_att ON t1_att@1 diffa_b@1 ; [t2_att@0]; t2_att@0; [diffa_b]; t1_att WITH diffa_b; I am somehow surprise that the Chi_Square is zero (which makes sense since the model is just identified), but the between SRMR is .oo4 (changing the estimator from MLR to WLSMV resolves the problem, but i can't explain why). Is something wrong with the syntax? Many thanks in advance! 


An SRMR value of 0.004 may be zero given the numerical/estimation precision. As for the syntax, please check with SEMNET. 


I am trying to do a latent change score model with a predictor variable: 'Bin_INSCHSUSP'. The data is complex (weighted with PSU and Strata). However, I get an warning message that says the PSI is not positive definite. Problem involving 'delta'. Please help. Analysis: Type = COMPLEX ; MODEL: !Latent Constructtime point one BIGmath1 BY X1MTHID X1MTHEFF (1) X1MTHINT (2); TOTmath1 BY BIGmath1*(3) X1TXMTH(4) zHiMath09(5); !Latent ConstructTime Point 2 BIGmath2 BY X2MTHID X2MTHEFF(1) X2MTHINT(2); TOTmath2 BY BIGmath2*(3) X2TXMTH(4) zHiMath12(5); !Correlate Errors X2TXMTH WITH X1TXMTH; zHiMath12 WITH zHiMath09; X2MTHID WITH X1MTHID; X2MTHEFF WITH X1MTHEFF; X2MTHINT WITH X1MTHINT; !Perform Latent Change Score TOTmath2 ON TOTmath1@1; delta BY TOTmath2@1; delta@0; [delta@0]; [TOTmath1@0]; [TOTmath2@0]; delta ON Bin_INSCHSUSP; Bin_INSCHSUSP WITH TOTmath1; TOTmath1 WITH delta; 


We need to see the full output  send to Support along with your license number. 

Rachel Jang posted on Thursday, October 04, 2018  10:09 am



This is the code. ANALYSIS:TYPE = MEANSTRUCTURE; COVERAGE = 0; ITERATIONS = 100000; MODEL = NOCOVARIANCES; MODEL: lx1 BY E0oci@1;lx2 BY E6oci@1; lx3 BY E12oci@1; lx4 BY E18oci@1; E0ociE18oci (sigma_x); [E0ociE18oci@0]; lx1;[lx1]; lx2lx4@0;[lx2lx4@0]; !lx1lx4@0;[lx1lx4@0]; lx2 ON lx1@1;lx3 ON lx2@1; lx4 ON lx3@1; dx2 BY lx2@1;dx3 BY lx3@1; dx4 BY lx4@1; dx2dx4@0;[dx2dx4@0]; dx2 ON lx1 (pi_x); dx3 ON lx2 (pi_x);dx4 ON lx3(pi_x); ly1 BY E0bu@1;ly2 BY E6bu@1;ly3 BY E12bu@1; ly4 BY E18bu@1; E0buE18bu (sigma_y);[E0buE18bu@0]; ly1;[ly1]; ly2ly4@0;[ly2ly4@0]; to be continued.. 

Rachel Jang posted on Thursday, October 04, 2018  10:11 am



Dear Dr. Muthèn: I ran LDS using the code below. However, I keep getting the error message (THE LATENT VARIABLE COVARIANCE MATRIX (PSI) IS NOT POSITIVE DEFINITE) and obtaining bad model fit. Is there anything I can do to remove the error message and improve model fit? Thank you so much for your help in advance! WARNING:THE LATENT VARIABLE COVARIANCE MATRIX (PSI) IS NOT POSITIVE DEFINITE.THIS COULD INDICATE A NEGATIVE VARIANCE/RESIDUAL VARIANCE FOR A LATENT VARIABLE, A CORRELATION GREATER OR EQUAL TO ONE BETWEEN TWO LATENT VARIABLES, OR A LINEAR DEPENDENCY AMONG MORE THAN TWO LATENT VARIABLES. CHECK THE TECH4 OUTPUT FOR MORE INFORMATION. PROBLEM INVOLVING VARIABLE DX2. 

Rachel Jang posted on Thursday, October 04, 2018  10:12 am



This is the code. ANALYSIS:TYPE = MEANSTRUCTURE; COVERAGE = 0; ITERATIONS = 100000; MODEL = NOCOVARIANCES; MODEL: lx1 BY E0oci@1;lx2 BY E6oci@1; lx3 BY E12oci@1; lx4 BY E18oci@1; E0ociE18oci (sigma_x); [E0ociE18oci@0]; lx1;[lx1]; lx2lx4@0;[lx2lx4@0]; lx2 ON lx1@1;lx3 ON lx2@1; lx4 ON lx3@1; dx2 BY lx2@1;dx3 BY lx3@1; dx4 BY lx4@1; dx2dx4@0;[dx2dx4@0]; dx2 ON lx1 (pi_x); dx3 ON lx2 (pi_x);dx4 ON lx3(pi_x); ly1 BY E0bu@1;ly2 BY E6bu@1;ly3 BY E12bu@1; ly4 BY E18bu@1; E0buE18bu (sigma_y);[E0buE18bu@0]; ly1;[ly1]; ly2ly4@0;[ly2ly4@0]; To be continued.. 

Rachel Jang posted on Thursday, October 04, 2018  10:13 am



ly2 ON ly1@1;ly3 ON ly2@1; ly4 ON ly3@1; dy2 BY ly2@1;dy3 BY ly3@1; dy4 BY ly4@1; dy2dy4@0;[dy2dy4@0];!set means and var to 0 dy2 ON ly1 (pi_y); dy3 ON ly2 (pi_y);dy4 ON ly3 (pi_y); dy2 ON lx1 (delta_y); dy3 ON lx2 (delta_y); dx2 (dd_y); dy4 ON lx3 (delta_y) dx3 (dd_y); dx2 ON ly1 (delta_x); dx3 ON ly2 (delta_x) dy2 (dd_x); dx4 ON ly3 (delta_x) dy3 (dd_x); OUTPUT: tech1 tech3; SAMPSTAT; thank you! 


Please send your output to Support along with your license number. We ask that postings be limited to one window. 

Daniel Lee posted on Wednesday, December 26, 2018  8:32 am



Hi Dr. Muthen, Are there any Mplusrelated manuscripts or videos that cover the inclusion of distal outcomes in latent difference score models? I would like to estimate a model where the latent difference scores predict a dependent variable. Is the syntax as simple as just including one additional line of syntax indicating the following (deta is the latent difference scores): Y on deta2 deta3 deta4 ; Thanks much for your help! 


Yes, that should do it. 

Daniel Lee posted on Friday, May 17, 2019  9:11 am



Hi Dr. Muthen, I have a hopefully quick question about a a latent change score model with covariates. If the effect of a covariate (x) on the latent change variable is positive, but the mean of the latent change variable is negative, does that mean that the covariate is contributing to a larger decrease in the change variable from y(t1) to y(t)? Thank you! 


No, a smaller decrease. Increasing x gives an increase to the DV so less negative. The easiest way to understand it is to try some different x values. 

Daniel Lee posted on Monday, May 20, 2019  7:44 am



Thank you! 

AMN posted on Thursday, July 25, 2019  8:08 am



Dear Drs. Muthen, I am conducting a latent change score model and have a question about the use of transformations across waves. Out of my four weeks of data, only one week's data had serious skew, which led me to perform a square root transformation. My question: is it acceptable to use the original (untransformed) data for 3 of the weeks and the transformed data for the one week that had a skew? I was not sure if all of the weeks' data needed to undergo a square root transformation so that the range was consistent or if the transformation would not affect the analysis of change scores. Thank you! 


I would not transform for just one time point. But these are general analysis strategy questions suitable for SEMNET. 

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