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Hi support team, I am running a CFA across three waves of longitudinal data. I would like to follow the approach by A. Farrel 1994, to test consistency of the measurement model across time. Therefore I need the factor loadings of the latent constructs to be equal across each time point. How can I model this with Mplus, if I do not run a multiple group CFA and handle three times points as three groups? Thank you for your help!! 


Please see the multiple indicator growth example in the Topic 4 course handout. The first part of the example tests for measurement invariance across time. It is not correct to use the three time points as three groups because the groups would not be independent. 

Elan Cohen posted on Tuesday, August 23, 2011  8:03 am



Dr. Muthen, I'm trying to run a longitudinal CFA over 15 years of data. There are 50 items per year (all dichotomous), 1200 observations, and 2 latent factors per year. 1. Does this seem feasible? (It seems like too many variables and not enough observations to me). 2. Could you tell me if the following input will give me the correct model (shown only for 3 years of data). MODEL: f1a5 by item1a5item25a5; f2a5 by item26a5item50a5; f1a6 by item1a6item25a6; f2a6 by item26a6item50a6; f1a7 by item1a7item25a7; f2a7 by item26a7item50a7; item1a5item25a5 pwith item1a6item25a6; item26a5item50a5 pwith item26a6item50a6; item1a6item25a6 pwith item1a7item25a7; item26a6item50a6 pwith item26a7item50a7; Thank you very much. 


With that many items and time points, I would try a twolevel approach. You would then have 50 variables and 15 members (max) per cluster, where cluster is id (subject). This preassumes measurement invariance across time. You can then specify a random intercept and slope which vary across subjects to see how factor means change over time. You can look at UG ex9.16 and combine it with ex9.15. 

Susan Pe posted on Monday, June 25, 2012  12:33 pm



I am using a Panel data with 57 firms over 30years (each year 16 observations, not all firms have 16 observations). I am trying to do CFA, but not sure if this is correct. Other than observed measures, I add under VARIABLE CLUSTER IS firms; ANALYSIS: TYPE IS TWOLEVEL; I am not sure about %within% and %between% commands, and which is more appropriate. I am also not sure if I need to add within = TIME. I am not sure whether I should fix the latent variable @1 either. Thank you!!! 


There are many ways to do this, but let me ask you some questions first. How many items are you considering at each time point and are they continuous or categorical? Note also that longitudinal data need not be analyzed as twolevel, but can be handled in a singlelevel approach where a wide instead of a long format is considered. See our handouts for Topics 34 in our courses. 

Susan Pe posted on Tuesday, June 26, 2012  2:47 am



I have 7 items, some are continuous and some are categorical. Given that I have over 12000 observations x 7items over 500 different time points, do you think using a singlelevel approach with a wide format is doable? 


No, 500 time points is not doable in wide form in the current Mplus. In the current Mplus version you want to take a twolevel approach: time and firms. This has the disadvantage that you have to assume measurement invariance across time. In the upcoming Version 7 of Mplus, however, there will be more choices, such as a 3level approach and also a the choice of allowing random forms of measurement noninvariance. 

Susan Pe posted on Wednesday, June 27, 2012  7:24 am



Thank you so much for your reply. Do you think I can do this in long format with cluster = firm; within = time ; analysis: type = twolevel random; model: %within% latent variables by observed variables; But, how do I incorporate time under model? Also, the gap between different time points are typically 2 weeks, but is longer when the year changes (couple of months). I see it in the example that time is written in the data as 0,1,2,3... Is it a problem that the time between observations varies? Is it possible to write time as dates? 


See Example 9.16 for the long format. 

Susan Pe posted on Tuesday, August 28, 2012  2:16 pm



Hi I saw the example but it's still not clear. Is this command correct? cluster = firmid; Analysis: Type = twolevel; Model: %within% RD by item1 item2 item3; I don't need specify between? 


Example 9.16 is a growth model. You are showing a factor model. What exactly are you trying to do? 

Susan Pe posted on Wednesday, August 29, 2012  2:06 pm



I want to just confirm the factor structure by doing a cfa, not estimate a growth model. I have panel data but due to too many time points I cannot do wide format, so I opted for two level model. Level 1 (WITHIN) is data points over time, level 2 (BETWEEN) is firms. I want to validate my factor structure with a confirmatory factor analysis, using longitudinal data. I am not particularly interested in BETWEEN and WITHIN level differences. So I am not sure which factor scores to look at or whether I am using the commands 


If you have a measurement instrument that is given at many time points, you can do twolevel factor analysis with data in long format. This assumes meas. invar. across time. You say: %within% fw by y1y10; %betweeen% fb by y1y10; although you can have a different number of factors on the two levels. 

June Zhou posted on Wednesday, November 07, 2012  7:47 am



I have a question on interpretation of longitudinal invariance CFA results. Can I interpret as "The responses on items are consistent across time given that the intercept invariance or strong invariance is hold (factor loading and thresholds were constrained)"? 


If you have intercept and factor loading invariance, you can say that. 

June Zhou posted on Sunday, November 11, 2012  9:24 am



Thank you so much for your reply, Dr. Muthen. 

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