Message/Author 

Shige Song posted on Tuesday, October 26, 2004  10:56 am



Dear Linda and Bengt, I have a question of the concept of the "individuallyvarying times of observation". Say, I have three panels of the same group of people with two years between each panel. The respondents are of different age groups (from age 1 to age 10), and they were interviewed at different time points (for example, some were interviewed in July and some were interviewed in August). The simplest model will be to ignore the fact that these people are of different age group and do this: ... Model: i s  y11@0 y12@1 y13@2; ... However, I want to make this model more realistic and take into consideration of the fact that people are from different age groups, should I use this "individuallyvarying times of observation" approach as discussed in pp.9294 in the MPlus manual? I am thinking something like this: ... Variables: ... Tscores = age1 age2 age3; Analysis: Type = Random; Model: i is  y1 y2 y3 AT age1 age2 age3; ... where age1age3 are the newly generated variables that represent the exact age of each individual at the time of interview. Have I got this idea right? Thanks! Shige 


It sounds right. 

Shige Song posted on Tuesday, October 26, 2004  7:24 pm



Hi Linda, If that's the model I think it is, then I have a problem estimating it. I got the error message: THE ESTIMATED COVARIANCE MATRIX IS NOT POSITIVE DEFINITE AS IT SHOULD BE. COMPUTATION COULD NOT BE COMPLETED. PROBLEM INVOLVING VARIABLE S. THE MODEL ESTIMATION DID NOT TERMINATE NORMALLY DUE TO AN ERROR IN THE COMPUTATION. CHANGE YOUR MODEL AND/OR STARTING VALUES. I estimated the same model using Stata Gllamm and MlwiN (as multilevel model) and they both worked ok and gave me roughly the same estimates. Now I am trying to figure what caused the problem of "NOT POSITIVE DEFINITE" in MPlus but not in Gllamm or MlwiN. Do you have any ideas? Thanks! Shige 


I would have to see the output from Glamm or MLwiN and Mplus to answer that question. I think that they hold the residual variances of the outcome equal across time and Mplus does not so therefore the models are different. Also, they may simply not print the message that the matrix is not positive definite. If you send the outputs to support@statmodel.com, I will answer the question more fully. 

Shige posted on Wednesday, October 27, 2004  9:45 am



Hi Linda, It turns out that I have not set up the data correctly. After I reorganized my data set, now MPlus gives me roughly the same results as the other two packages. Shige 

Shige Song posted on Thursday, December 30, 2004  10:19 am



The model I estimated above seems to be a linear growth model in the multilevel sense (the estimates are not exactly identical to what are from GLLAMM and Mlwin, but close enough). Now, I want to estimate a quadratic growth model with individually varying time of observation, what should I do? I have been searching the web for quite a while, but could not find any examples. I tried: … Analysis: Type = random missing; Model: i s1  height89 height91 height93 at age89 age91 age93; i s2  height89 height91 height93 at age89_2 age91_2 age93_2; … Where age89_2=age^2, age91_2=age91^2, age93_2=age93^2. But I got the error message: … *** ERROR in Model command Random slopes previously defined: I S2 … Why is this? Thanks! Shige 


See the AT option of the MODEL command. For a quadratic model, you need three growth factor names. 

Shige Song posted on Friday, December 31, 2004  7:55 am



Hi Linda, Thanks, that's very helpful! Can you also tell me where I can find some references on estimating piecewise growth model with individually varying time of observations using Mplus? Examples from the manual and course reader deal with these two issues (that is, piecewise growth model and growth model with individually varying time of observations) separately. I've been trying to put them together to do a piecewise growth model with individually varying time of observations without luck. Thanks! Happy new year! Best, Shige 

bmuthen posted on Friday, December 31, 2004  8:00 am



Best wishes for the new year in Beijing, Shige. I am not aware of references that cover this combination. Perhaps you can contact Paras Mehta at the U of Houston to see if he knows. But I'd be happy to take a look at your example to see if I can figure it out. 

Shige Song posted on Friday, December 31, 2004  10:26 am



Hi Bengt, Thanks! I will try to contact Paras Mehta and see if he has done something on this topic. Meanwhile, I have estimated a piecewise growth model using Stata+Gllamm and try to estimate an equavalent model using Mplus. I plan to spend some more time on this and try different possibilities before sending you anything. I have a more general question at this moment though. Without individually varying time points, Mplus is extremely felxible in handling nonlinear growth pattern (which as I understand has something to do with the SEM approach toward growth problem). One can estimate many type of models including linear, quadratic, piecewise linear, logistic, ...etc. However, when there are individually varying time points involved, the choices are limitted: intercept, linear, quadratic, and cubic (Pp. 458). My question is: if none of the above four models produces good enough fit to the data (which is indeed true in my case), what should I do next? Piecewise linear model is one possibility, and there may be others. But again the presence of individually varying time points makes things much more complicated... Thank you very much, and happy new year! Best, Shige 

bmuthen posted on Friday, December 31, 2004  10:54 am



I think Mplus Discussion has had the issue of individuallyvarying times of observations (using the Mplus "AT" option) together with piecewise before and we presented a solution  but I can't remember exactly what it was, but you can certainly do piecewise and AT using 2 separate sets of intercepts and slopes for the two pieces and then hold parameters equal for growth factors assumed to be the same. For instance if you have the intercepts i1 and i2 for the 2 pieces, you can have the equality constraints: [i1 i2] (1); i1 i2 (2); etc for covariances and regression slopes. On the other matter of flexibility, it sounds like you want to have the combination of the SEM estimation of time scores (treating them as parameters that do not vary across people) and the multilevel practice of entering time scores as data rather than parameters. This combination would in principle seem possible, at least if individuals at the same approximate timing could be said to have the same time score parameter to be estimated  I have not seen this idea carried out, but if it is identified I would think it can be done in Mplus. 


You could also use ON instead of AT to deal with this issue: i by y1y3@1; s1  y1 on t1; s1  y2 on t2; s1  y3 on t3; s2  y1 on t12; s2  y2 on t22; s2  y3 on t32; y1 with y2y3@0; y2 with y3@0; 

Shige Song posted on Saturday, January 01, 2005  8:08 pm



Hi Linda & Bengt, Thanks for the help! I tried Linda's approach. I begin with a simple example to check if Linda's approach reproduces exactly what we know the correct output. Here is the "correct" code: ... Model: i s1  h89 h91 h93 at a89 a91 a93; ... and here is Linda's approach: ... Model: i by h89 h91 h93@1; s1  h89 on a89; s1  h91 on a91; s1  h93 on a93; h89 with h91h93@0; h91 with h93@0; ... But they did not procude exactly the same results. For example, the "correct" model has DF of 8 and Linda's approach has DF of 10; parameter estimates are not identical either (close though). I also tried Bengt's suggestion as this: ... Model: i1 s1  h89 h91 h93 at a89 a91 a93; i2 s2  h89 h91 h93 at a89_2 a91_2 a93_2; i1 i2 (1); [i1 i2] (2); ... where a89_2 a91_2 a93_2 are squared terms of a89 a91 a93 (generated in Stata). But I got error message: THE ESTIMATED COVARIANCE MATRIX IS NOT POSITIVE DEFINITE AS IT SHOULD BE. COMPUTATION COULD NOT BE COMPLETED. PROBLEM INVOLVING VARIABLE S2. THE MODEL ESTIMATION DID NOT TERMINATE NORMALLY DUE TO AN ERROR IN THE COMPUTATION. CHANGE YOUR MODEL AND/OR STARTING VALUES. The post Bengt mentioned is this (I think): http://www.statmodel.com/discussion/messages/14/478.html?1096047165 but there is only a question without answer. By the way, Mplus is an amzaing software, the more I learn, the more I want to learn. Happy new year! Shige 


One mistake in my suggestion is that you don't have all of the factor loadings for i fixed at one. You should change i by h89 h91 h93@1; to i by h89@1 h91@1 h93@1; or i by h89h93@1; I would then suggest asking for TECH1. This will show you the free parameters in Mplus for your model. Then compare this to the free parameters in whatever you are comparing to. If you make the model parameters the same, you will most likely get the same results. 

bmuthen posted on Sunday, January 02, 2005  9:56 am



Linda will answer your 3 specific questions, but let me raise a more general issue. In answering your specific questions, I lost track of what your questions originated from. Looking back at your earlier message, it seems like you have people measured 3 times but you have different age groups in your data. I wonder how many distinct ages are represented in your data and in relation to this, have you considered the following two approaches instead of using "AT"? (1) a multiplecohort (multigroup) analysis of the age groups. (2) stringing out your outcomes as one per age, where each age group has missing data at some ages. I would be interested in seeing a table of your data structure layed out like the NLSY data on page 98 of the Mplus growth modeling handout ("Day 2") that you have. Note also that with only 3 time points per person, general piecewise modeling can't be supported  you should have at least 3 time points for each of the two pieces since each piece is its own growth model. Otherwise, it seems you have to work with a piecewise model that has strong parameter restrictions, e.g having a fixedeffect secondpiece slope and all other parameters the same for the two pieces. But this is not a good way to handle fitting of 3 time points, I think. I would as a first step consider approach (1) above. 

bmuthen posted on Sunday, January 02, 2005  9:59 am



Regarding the specifics in trying my suggestion, note also that the message THE ESTIMATED COVARIANCE MATRIX IS NOT POSITIVE DEFINITE AS IT SHOULD BE. COMPUTATION COULD NOT BE COMPLETED. PROBLEM INVOLVING VARIABLE S2. indicates that s2 may have a close to zero variance  check the output. If so, make s2 a fixed effect by fixing its variance to zero, s2@0; 


Can I use individuallyvarying times of observation in a growth mixture model with categorical indicators? 

bmuthen posted on Friday, May 20, 2005  11:03 am



Yes. 


So, can I do something like this? PHYS2 BY doe8at2 doe16at2 doe22at2 doe23at2 doe24at2 doe25at2; PHYS3 BY doe8at3 doe16at3 doe22at3 doe23at3 doe24at3 doe25at3; PHYS4 BY doe8at4 doe16at4 doe22at4 doe23at4 doe24at4 doe25at4; PHYS5 BY doe8at5 doe16at5 doe22at5 doe23at5 doe24at5 doe25at5; PHYS6 BY doe8at6 doe16at6 doe22at6 doe23at6 doe24at6 doe25at6; i s  phys2phys6 AT age2age6; Where doe are categorical indicators measured at timevarying points that are stored in the age variable? 

bmuthen posted on Saturday, May 21, 2005  8:23 am



Yes, Mplus can handle this. But note that you should have measurement invariance across time for this to make sense because a given measurement occasion is at different times for different people. 


When I use this syntax: USEVARIABLES ARE contsym1 contsym2 contsym3 contsym4 contsym5 aget1 aget2 aget3 aget4 aget5; TSCORES ARE aget1 aget2 aget3 aget4 aget5 ; ANALYSIS: type = random missing ; MODEL: i s contsym1 contsym5 AT aget1  aget5; where contsym1  contsym5 are continuous variables and aget1aget5 are the individual ages for the people in the sample  this seems to work. However, this syntax: USEVARIABLES ARE contsym1 contsym2 contsym3 contsym4 contsym5 aget1 aget2 aget3 aget4 aget5; TSCORES ARE aget1 aget2 aget3 aget4 aget5 ; ANALYSIS: type = random missing ; MODEL: i s  contsym1 contsym2 contsym3 contsym4 contsym5 at aget1 aget2 aget3 aget4 aget5; OUTPUT: sampstat; Generates this error: *** ERROR in Model command The number of fixed time scores is not sufficient for model identification in the following growth process: I S I thought that those two syntaxes were identical and don't know what is going wrong. I am also having trouble installing the patch to upgrade to version 3.12. I wasn't sure if I had the base + combination addon, but if I try the others, I get an error that I have an invalid Mplus.exe in my path environment. When I try the combination, it starts to go through installing, but then says I need to have Mplus Base 3.0 +Combination installed. Thanks for the help, Jennie 


Please send your message to support@statmodel.com. These questions are better answered in that way. 


Dear Dr.'s Muthen, Is it possible to extend the growth model from example 6.12 (current user's manual; Growth model with indivually varying times of observation) into the GGMM framework using Mplus? Thanks! 


Yes. 

wendy posted on Monday, July 17, 2006  3:13 pm



Hi,Dr. Muthen: I would like to use NLSY data to conduct my research and do you know how to assess to NLSY dataset from UCLA web? I need a UCLA faculty sponsor to receive a guest ID. Thanks for your help 


I don't know. But you can buy the NLSY CD for about $20 from the originators at the Ohio State Univ. 


Do you know of any journal or technical references that address "individuallyvarying times of observation" in the Mplus latent variable modeling framework?  Thanks 


Following are two references that can be found on the website under Papers: Muthén, B. & Asparouhov, T. (2006). Growth mixture analysis: Models with nonGaussian random effects. Forthcoming in Fitzmaurice, G., Davidian, M., Verbeke, G. & Molenberghs, G.(eds.), Advances in Longitudinal Data Analysis. Chapman & Hall/CRC Press. Asparouhov, T. & Muthen, B. (2006). Multilevel mixture models. Forthcoming in Hancock, G. R., & Samuelsen, K. M. (Eds.). (2007). Advances in latent variable mixture models. Charlotte, NC: Information Age Publishing, Inc. 


Hi  I am running growth models on 5 time points of data. When I ran the models using fixed time points I determined that a three growth factors (i.e., the inclusion of a quadratic term) resulted in significantly better model fit. In switching to individuallyvarying times of observation I found that my models run fine with only intercept and slope factor estimates but do not converge with the inclusion of the quadratic. I'm pretty sure my syntax is correct: USEVARIABLES ARE rwDtotT0 rwDtotT2 rwDtotT4 rwDtoT10 rwDtoT16 ctimwT0 ctimwT2 ctimwT4 ctimwT10 ctimwT16; Tscores are ctimwT0 ctimwT2 ctimwT4 ctimwT10 ctimwT16; ANALYSIS: TYPE = random missing; MODEL: i s q rwDtotT0rwDtoT16 AT ctimwT0ctimwT16; The error message is: THE ESTIMATED COVARIANCE MATRIX IS NOT POSITIVE DEFINITE AS IT SHOULD BE. COMPUTATION COULD NOT BE COMPLETED. THE RESIDUAL CORRELATION BETWEEN S AND I IS 1.000 THE MODEL ESTIMATION DID NOT TERMINATE NORMALLY DUE TO AN ERROR IN THE COMPUTATION. CHANGE YOUR MODEL AND/OR STARTING VALUES. In general, what would you recommend to fix this problem? thanks for your help! Cindy Schaeffer 


Can I have a growth model in which I use individuallyvarying times of observation for the estimates of i and s, but fixed time estimates for q (the quadratic growth factor)? I have tried this using the following model command: ANALYSIS: TYPE = random missing; MODEL: i s  rwDtotT0rwDtoT16 AT ctimwT0ctimwT16; q  rwDtotT0@0 rwDtotT2@1 rwDtotT4@4 rwDtoT10@25 rwDtoT16@64; but get the error: MAXIMUM LOGLIKELIHOOD VALUE FOR THE UNRESTRICTED (H1) MODEL IS 1590.808 THE MODEL ESTIMATION DID NOT TERMINATE NORMALLY DUE TO AN ILLCONDITIONED FISHER INFORMATION MATRIX. CHANGE YOUR MODEL AND/OR STARTING VALUES. THE MODEL ESTIMATION DID NOT TERMINATE NORMALLY DUE TO A NONPOSITIVE DEFINITE FISHER INFORMATION MATRIX. THIS MAY BE DUE TO THE STARTING VALUES BUT MAY ALSO BE AN INDICATION OF MODEL NONIDENTIFICATION. THE CONDITION NUMBER IS 0.363D15. THE STANDARD ERRORS OF THE MODEL PARAMETER ESTIMATES COULD NOT BE COMPUTED. THIS IS OFTEN DUE TO THE STARTING VALUES BUT MAY ALSO BE AN INDICATION OF MODEL NONIDENTIFICATION. CHANGE YOUR MODEL AND/OR STARTING VALUES. PROBLEM INVOLVING PARAMETER 7. thanks again, Cindy Schaeffer 


You cannot combine fixed and individuallyvarying times of observation. When you have these types of problems, please send your input, data, output, and license number to support@statmodel.com. 


Why is it not ok to combine fixed and individually varying time scores? I have done this in the past without problems with convergence... Thanks Michelle Little 


Time scores cannot be both parameters and data in the same model. They can play only one of these roles. I'm not sure if this is what you mean. I would have to see exactly what you did to say more. If you would like, please send your output and license number to support@statmodel.com. 

Tim Stump posted on Friday, October 09, 2009  6:17 am



When specifying a model in Mplus with individuallyvarying times of observation, can the number of observations for each subject be different? That is, can one subject contribute 8 observations while another contributes 5 and another only contributes 2? 


Yes. This is done using missing data for the measurements that observations were not present for. 


Dear Linda, I would like to fit a twolevel growth model with individual specific timescores. Can this be done in Mplus? Previous analyses show that both the use of the individual timescores (if I disregard the twolevel design) is important as well as the twolevel design (using fixed regular timescores). I was looking for a way to do a 3level analysis on a long dataset, but I can't find an example in the user's guide. Kind Regards, Ruben. 


Threelevel analysis can be done only if one level is repeated measures in a wide format. See Example 9.12. The AT option allows for individuallyvarying times of observation. 


I think I managed. I didn't realize that the different analysis types (complex and random) could be combined. I only used those combinations that were used in de User's Guide. This is the code, and it worked as expected. Do you think I makes sense? And how to compare this model with a model with fixed time points? The fit indices are not comparable. But is there something else that could help me to make an educated guess what the best model is? Tscores = tijd_1  tijd_3; cluster = hh; analysis: type = random complex; model: i s  qol_1 qol_2 qol_3 at tijd_1  tijd_3 ; i s on bel_reg EOO vrouw age werk income conflict auton i_beide i_ex ; 


This seems correct. I would however fit the growth model before I added covariates. See the ESTIMATOR option in the user's guide where all combinations of the TYPE option are shown. 


Hi Linda, I am testing a model with individually varying times of observation. The model below includes three points of data collection (T1, T3, T5), with ages ranging from 1216 at time 1 1418 at time 5 (in order to use whole numbers for age, since data was collected every 6 months, I only used three of 5 points). T1numparT5numpar refers to number of sexual partners at each time. USEVARIABLES ARE T1numpar T3numpar T5numpar T1age T3age T5age; MISSING ARE blank; TSCORES = T1ageT5age; ANALYSIS: TYPE = RANDOM; MODEL: i s  T1numpar T3numpar T5numpar AT T1ageT5age; T1numpar with T3numpar T5numpar; First, am I correct that I actually have 7 time points in this model (reflecting ages 1218 across the time points)? And the resulting slope represents change over age rather than over time of data collection? And intercept represents the number of partners at age 12 (not time 1)? Second, when I request plot 3, only the three data collection points are represented  is there a way to get a plot that reflects age as the time point? Also, as a related question, is there a way to generate a plot of the mean intercept and slope? Finally, is there a way to evaluate model fit based on the loglikelihood value, and if so, could you point me to a reference? Thank you for your help!! Helen 


1. The model is estimated over age so you have 7 time points. 2. Mplus does not plot growth curves when time scores are used. You would need to do that outside of Mplus. 

Alden Gross posted on Thursday, March 10, 2011  11:07 am



Dear Linda and Bengt, I hope to estimate a sequential/piecewise growth model with data in long format (thus, TYPE = TWOLEVEL;) because time is continuous and persons are seen at irregularly spaced intervals. How can I estimate such a model with piecewise growth? I am looking for a marriage of UG Examples 6.11 and 9.2. Am I on the right track with the following? model: %within% s1  y ON timea; s2  y ON timeb; %between% [y]; [s1]; [s2]; s1 s2 WITH y; DEFINITIONS timea=time if time<=5, 0 otherwise timeb=time if time>5, 0 otherwise Thanks much! Alden 


I haven't tried this, but it looks right. If time goes high, you may want to divide by 10. 

Alden Gross posted on Saturday, March 12, 2011  10:14 am



Thanks! See you in Baltimore. 

Huiping Xu posted on Tuesday, November 15, 2011  11:04 am



Dear Linda and Bengt, Can we do individually varying time of observations in growth mixture models? I have subjects measured at different ages and would like to find different developmental patterns. This is what I tried for a twoclass model: VARIABLE: NAMES ARE y1y4 t1t4; USEVAR = y1y4; TSCORES = t1t4; CLASSES = c(2); MISSING = ALL (999); ANALYSIS: TYPE = MIXTURE missing; MODEL: %OVERALL% i s  y1y4 AT t1t4; IS@0; But it produces an error message: *** ERROR in VARIABLE command TSCORES option is only available with TYPE = RANDOM. Could you please point me to the right direction? Thanks a lot. Huiping 

Huiping Xu posted on Tuesday, November 15, 2011  11:41 am



I figured it out. Instead of ANALYSIS: TYPE = MIXTURE missing, I have ANALYSIS: TYPE = MIXTURE RANDOM missing and it worked. Thanks. 

Sam Hyun Yoo posted on Thursday, November 17, 2011  6:08 pm



Dear Linda and Bengt, With NLSY79 data, I was trying to run growth curve model and encountered an error. I have eight cohorts for 17 waves, and time intervals are unequally spaced (12 years) unbalanced design. With TSCORE option. I was trying to use 'individually varying time score. (also considering a count outcome) Could you let me know what the problem is? Best, Sam DATA: FILE IS LCMBASELINE.dat; VARIABLE: MISSING = ALL (1234); NAMES = *** (omit); USEVARIABLES = *** (omit) ; TSCORES = TS79 TS82 TS83 TS84 TS85 TS86 TS88 TS90 TS92 TS94 TS96 TS98 TS00 TS02 TS04 TS06 TS08 ; COUNT = EXP79 EXP82 EXP83 EXP84 EXP85 EXP86 EXP88 EXP90 EXP92 EXP94 EXP96 EXP98 EXP00 EXP02 EXP04 EXP06 EXP08 ; ANALYSIS: TYPE=RANDOM; MODEL: I S EXP79 EXP82 EXP83 EXP84 EXP85 EXP86 EXP88 EXP90 EXP92 EXP94 EXP96 EXP98 EXP00 EXP02 EXP04 EXP06 EXP08 AT TS79 TS82 TS83 TS84 TS85 TS86 TS88 TS90 TS92 TS94 TS96 TS98 TS00 TS02 TS04 TS06 TS08 ; I S ON NSIBLING HISP BLACK ; OUTPUT: SAMPSTAT MODINDICES TECH1 TECH8 ; Plot: type = plot3; *** ERROR in MODEL command Observed outcomes in a growth process must be measured on the same scale. Problem with: I S 


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

Joe posted on Monday, November 26, 2012  10:13 am



Hello: Is it acceptable to compare the fit indices (AIC, BIC, and ABIC) between a "regular" growth model using ML estimation with fixed time scores (e.g., 0 1 2 3 4) , and a growth model using "TYPE=RANDOM" with individuallyvarying time scores? Or do the model estimations use a different covariance structure and make comparisons unacceptable? Thanks, Joe 


These models have the same set of dependent variables. You can compare them using BIC because the metric of the BIC's are the same. The models are not nested. 

Ashley Hum posted on Saturday, September 07, 2013  2:23 pm



Hi, I am trying to run a growth model with individuallyvarying times of observation after using multiple imputation to address missing data. I have 5 years of data, the first 2 years were actually collected at the same time point (thus all time data is the same across participants), but the latter time points were collected at different time points (thus the time since baseline differs across individuals). When I run the below input, the output that comes up only shows my syntax. Could you please advise on how to correct the syntax so the model will run? Data: File is "imp3list.dat"; TYPE= IMPUTATION; Variable: Names = ASH98M ASH99M ASH02M ASH03M ASH04M TS98 TS99 TS02 TS03 TS04; usevariables = ash98m ash99m ash02m ash03m ash04m ts98 ts99 ts02 ts03 ts04; tscores = ts98 ts99 ts02 ts03 ts04; Missing = all (99); Analysis: type = random; estimator = ML; Model: i s  ash98m ash99m ash02m ash03m ash04m AT ts98 ts99 ts02 ts03 ts04; Thanks, Ashley 


Please send your input, data, and license number to support@statmodel.com. 

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