

Time scores associated with slope gro... 

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Anonymous posted on Friday, September 20, 2002  10:56 am



The time scores (loadings) associated with a slole growth factor in LGM can be set as 0, 1, a3, ... aT (Muthen, et al., 2000), where the time score a1 is fixed at 0, defining the intercept growth factor as baseline initial status at t1; and the time scores for t3 and later time points are set to vary freely. However, the time score a2 is fixed at 1 for t2. I guess, this has something to do with parameter idenfication (if a2 were set free as are the loadings for t3, t4, ..., the model won't run). Can you explain the statistical rationale on this issue? In addition, if we set a3=0, while free a1 and other loadings, which loading should be set to 1? Thanks a lot for your help. 


For identification purposes, one time score in addition to the zero time score for the intercept growth factor must be fixed to a nonzero value. This defines the metric of the slope factor as the change between the two fixed timepoints. If you fix the time score for the third time point to 0, the time score you fix to a nonzero value can be any of the other time scores. 

Wim Beyers posted on Monday, May 05, 2003  7:50 am



Suppose a classic latent growth function summarizing 3 repeated measures (with equally spaced time points) of an attribute, with a linear shape, and centered at the first measurement, so the interpretation of the intercept is the true (without measurement error)initial level of the attribute (at Time 1), and the slope refers to the linear change of the attribute across time. Now, I want to recenter my growth function at the second measurement (by changing the fixed loadings of the slope to 1, 0, 1). The meaning of the slope stays the same, but the meaning of the intercept now becomes the true score at Time 2. So far, so good. However, is it true that the more substantive interpretation of the intercept now is the true mean level of the attribute across time, or let's say, the overall or basic level? Of course, given the above mentioned restrictions of linear change and equally spaced time points? And, if yes, do you agree that recentering therefore is a good thing when you have three repeated measures in a timestructured format as mentioned? Thanks for all comments and for your previous replies to my questions, Wim Beyers Belgium 

bmuthen posted on Monday, May 05, 2003  10:25 am



Sounds right given the time scores of 1, 0, 1. But it would seem to depend on the research question if this recentering is the most desirable. For instance, sometimes you want to predict the variation in the starting point, sometimes in the ending point. 

Li Lin posted on Thursday, September 02, 2010  1:04 pm



Hi,I am trying to mimic the example 12.9 using Monte Carlo simulation for a twopart growth model. My purpose of doing this is to decide an adequate sample size for a longitudinal study. Data will be collected at baseline, 1 month, 6 months, and 12 months. The PIs anticipate a growth curve like downupaccelerated up, for example: proportion of 1 in u = 1, .3, .5, .8; y equals to population mean at baseline, declines to mean2sd at 1 month, then up to mean1sd at 6 months, and then recover to mean at 12 months. I am thinking of using fixed time scores to specify the curve. My questions are: 1)what values I should give to the time scores for the above hypothesized change pattern? 2)do the time score sets need to be the same for u and y? Thanks! 


I think using fixed time scores to describe nonlinear growth in a simulation study is too strong of a hypothesis. I would instead consider a quadratic growth model. 


Dear Prof.Muthen, I apply parallel process LGM for mediation analysis. I have 4 time points (baseline, 8 months (post treatment), 12 months (1st follow up, and 20 months (last followup)). I am trying to model the earlier change in the mediator (from baseline to post treatment) and its effect on the later change in the outcome (from post treatment to the end of the 2nd followup). I am not sure if i do correct time coding in my models. Is the coding showed below correct coding for it? MODEL: i1 s1 ssb0lt@0 ssb1lt@1 ssb2lt@0 ssb3lt@0; i2 s2 bmi0@1 bmi1@0 bmi2@0.5 bmi3@1.5; p.s.The models work fine with this coding and fit well. Thank you so much beforehand for your help. 


No, those time scores are not right. For instance, the s1 scores should not be 0, 1, 0, 0 for regular piece wise, but 0, 1, 1, 1. But you can't do full 2piece growth modeling with only 2 time points per piece. The slope variances won't be identified. You could do this in a limited way in 2 parts instead: i1 s1  y1@1 y2@0; s1@0; so that you define i1 at the second time point. And then have i2 s2  y3@0 y4@1; s2@0; and then regress i2, s2 on i1 (s1 is not a variable since it has zero variance, so you can't regress on it). 


Thanks a lot Prof.Muthen. I changed the time coding for the mediator to 0 1 1 1; i1 s1 ssb0lt@0 ssb1lt@1 ssb2lt@1 ssb3lt@1; For the outcome, actually I do not use only 2 time points as you mentioned in your message. I only change the intercept to the post treatment and reflect the change after post treatment; i2 s2 bmi0@1 bmi1@0 bmi2@0.5 bmi3@2.5; When I apply my parallel process LGM (with 1000 bootstrapping), the model fits good and gives the slope variances (in my case residual variances since I have covariates in the model too). MODEL: i1 s1 ssb0lt@0 ssb1lt@1 ssb2lt@1 ssb3lt@1; i2 s2 bmi0@1 bmi1@0 bmi2@0.5 bmi3@2.5; i1 s1 ON group gender ethnic; i2 s2 ON group gender ethnic; s2 ON i1 s1; s2 ON i2; s1 ON i2 i1; i1 WITH i2; group WITH gender ethnic; MODEL INDIRECT: s2 IND s1 group; Is this method and coding right for PPLGM for mediation analysis? Thank you. 


Dear Prof.Muthen, I think i made a mistake in my previous message; For the outcome variable I believe that I should model a regular LGM to reflect 0, 8, 12 and 20 months measurements, as; i2 s2 bmi0@0 bmi1@1 bmi2@1.5 bmi3@2.5; But for the outcomes that have a quadratic growth, I think I should make this coding as 'time*time'as it was suggested in the book of Singer and Willet 2003 (Applied longitudinal analysis)as; i2 s2 bmi0@0 bmi1@1 bmi2@2.25 bmi3@6.25 Is this fine to combine the LGMs as follows; i1 s1 ssb0lt@0 ssb1lt@1 ssb2lt@1 ssb3lt@1; i2 s2 bmi0@0 bmi1@1 bmi2@1.5 bmi3@2.5; the rest of the PPLGM model is the same as in the previous message. Thank you! Regards. 


You mention quadratic growth but don't show it, so I don't know what you mean about that. Regarding your statements: i1 s1 ssb0lt@0 ssb1lt@1 ssb2lt@1 ssb3lt@1; i2 s2 bmi0@0 bmi1@1 bmi2@1.5 bmi3@2.5; you can have different time scores for different growth factors. All that means is that the growth factor parameters are in different metrics, which is fine. 


Thanks for the reply, was helpful indeed. According to the growth shape (acceleration, deceleration) of the variable that has a quadratic growth, i use transformation of time and model it. It is explained as an alternative way to deal with nonlinear growth in the Applied Longitudinal Data Analyses book from Singer and Willett. An example of this coding was published by Ruehlman et al in Pain, 2012 Feb. 


Dear Professors, I am trying to fit a parallel LCGA: I1 S1CON_1@0 CON_2@.3 CON_3@.4 CON_4@.6 CON_5@.8 CON_6@.9 CON_7@.12; I1@0 S1@0; I2 S2  D10@0 D13@.3 D16@.6; I2@0 S2@0; CON_1 to CON_7 are measured at ages 4,7,8,10,12,13,16 D10D16 are measured at ages 10,13 and 16. I have two questions: 1) since D1016 are at ages 10,13 and 16 do they have to have the factor loadings the same as those for CON to represent the corresponding ages? I mean should they be D10@.6 D13@.9 D16@.12; I think the answer must be no, but I need to confirm this please with you and 2) when I want to quantify the average CON at age 7 do I multiply the estimate of the mean slope with 0.3 or with 3? Many thanks for your help and time to this matter. Kind Regards, Artemis 


The D variables do not use the time scores from the con variables. Use .3 if that is the time score in the estimated model. 


Many thanks this is really helpful. Kind Regards, Artemis 

KJ Research posted on Tuesday, January 26, 2016  7:18 am



Hi all, I collected data at equal time points over 6 weeks. I am testing a linear model and wondered what the implications are of testing: Model 1) i s  0 1 2 3 4 5 versus Model 2) i s  0 0.2 0.4 0.6 0.8 1 I believe that the mean slope for Model 1 pertains to the first two time points, whereas in Model 2 it can be interpreted across all six time points. Is that correct? If so, are time points 36 being 'ignored' in the first model? Many thanks in advance for your help. 


The time scores reflect the time differences in the measures. Both sets of time scores above reflect equidistant intervals. Either can be used. There is no difference. 

KJ Research posted on Tuesday, January 26, 2016  12:34 pm



Thanks Linda. I am questioning the different mean slope values in the two models. I read elsewhere that the mean slope changes depending on where you fix 0 and 1. Thus, if one opts for 'i s 0 1 2 3 4 5', does this mean that you are only assessing change from time point 1 to time point 2? If that is the case, what is happening with the remaining waves in this model? 


You should see the Topic 3 course video and handout on the website where the growth model is discussed in detail. The linear model as you show has an intercept and slope growth factor. The intercept growth factor is the systematic part of the variation in the outcome variable at the time point where the time score is zero. The slope growth factor is the systematic part of the increase in the outcome variable for a time score increase of one unit. In a linear model, the change is constant across time. The scale of the time scores does not change anything. The distance between the time scores is the only issue. 

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