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 Tiina Ojanen  posted on Tuesday, October 18, 2005 - 2:18 am
I'm conducting LGM with Mplus using three contsructs (each with 3 measurement points) as growth curves 1. social goals (multiple indicator curve), 2., withdrawal behavior (multiple indicator cureve) and social status, and interested in conducting regression among these constructs. I was wondering the following set of questions:

1) When wanting simply to indicate, that one construct (A) predicts increases in another construct (B) over time, which again predicts increases in another contruct (c), is it O.K. simply to predict the trend of B with a level of A, and the trend of C with the level of B?
Sometimes reseacrhes use the level of A to predict the level of B, and the trend of A to predict the trend of B, and so on. If I'm not interested in predicting change with a change, is the former approach suitable?

2) When setting linear trends as growht factors, is it common to stick to the original 0, 1, 2, loadings, even though there is a singificant negative mean for the trend, suggesting that there is a decrease rather than increase over time?
If so, then the results would be merely interpreted taking into consideration a decreasing rather than increasing trend? For instance, when wanting so show that the higher the level of goals, the higher the increases in withdrawal over time, there is a significant, negative estimate when predicting the (decreasing) trend of withdrawal with the level (intercept) of goals. Does this seem right? Given that the loading of 0 defines the level of a given construct, it would seem that if the trend was replaced with loadings of 2,1,0, the interpretation of the level would change?

3) How excatly are multigroup differences for gender conducted in the LGM framework? Are each of the estimated latent constructs, along with the estimated regression paths, tested individually by estimating them freely and constrained to be equal among genders (i.e., setting the variace of the given parameters equal accross the groups with a (1) marking in the syntax)?

4) I have defined a model including the three growth curves mentioned at the beginning, and have significant regression coefficients among the level of A and the trend of B, and the level of B and the trend of C., and almost O.K. model fit. However, due to negative variance of two of T1 and T3 withdrawal (latent) indicators, these were set to zero, after which the CFI dropped to .86. Given that RMSEA coefficient is O.K., this seems unfortunate. Is there something that I could do about this? For instance, have I forgot to fix some correlations os something, or should I do something for the starting values of the withdrawal curve? I have newer defined starting values before.

5) If a level of a trend is negative (esimate of the intercept mean is significantly negative), is this O.K., if the variable in question (measured in three time points) can have negative values (there is a growing trend in this construct with loadings 0, 1, 2)? Does this indicate that the average level of that contsruct is below zero?

Thank you so much in advance,
 bmuthen posted on Tuesday, October 18, 2005 - 7:05 pm
Here are quick answers that should be viewed critically since I don't know enough about your research situation and don't want to get into general consulting.

1) Certainly sounds reasonable. As long as the intercepts are allowed to covary.

2) All of that is correct and it is perfectly fine to stay with 0, 1, 2, ... even with a negative trend.

3) Yes, you put say (1) at the growth factor related parameters that you are interested in testing gender invariance for - such parameters are typically means and regression slopes.

4) One common reason for a misspecified multiprocess model is correlated residuals across processes - look at your Modification indices. Starting values shouldn't matter here.

5) Say that you have observed outcome values for an individual at the 3 time points of -1, -2, -3 and have a negative mean for the slope factor of -1. With time scores of 0, 1, 2 this still adds up fine since this models says that the outcome mean declines by 1 each time point (the mean change is the time score times the slope mean).
 Charles Saunders posted on Tuesday, November 15, 2005 - 1:44 pm

In an unconditional growth model that is set up in logs (i.e. ln(Y) = a + b(ln(Time)) - how do I interpret b and a? In OLS b would give the % change per % change in x - but how do I interpret that in terms of time? Thanks.
 bmuthen posted on Tuesday, November 15, 2005 - 5:53 pm
As ln(Time) changes one unit, ln(Y) changes b units. Note then that ln(Time) changing one unit corresponds to different time changes for different time levels since ln(X) is nonlinear in X. So you have to consider specific time intervals in the interpretation.
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