I have multidimensional construct where it makes no sense to add scores on a subscales into total score that can be measured over time and shown to change, ie rise or fall ;hence growth modeling may not be appropriate. A factor analyis showed that a five factor model provided the appropriate solution. I am trying to model transitions or shifts between factors in the factor model using covariates. Do you have any suggestions on how this might be done in MPLUS?
bmuthen posted on Tuesday, January 10, 2006 - 8:46 am
When you say transitions, I get the association of Latent Transition Analysis (see User's Guide for references). But LTA works with categorical latent variables, not continuous factors - this makes transitions between states possible. I am not clear on what you mean by "transitions between factors".
I thought about using LTA, and regime switching models,but
previous reseach using this survey showed that five factors emerged and each factor was labeled as a category into which people were forced based on their highest score on one of five dimensions/factors while other valuable information was disgarded. The literature in the area suggests that people can change between these labeled categories depending on situational factors.There are 56 items on the survey measured with a 5 point likert scale and as far as I know I will run in to problems with LTA in that Chi squared fit is impacted by the LTA table size. Secondly would I not have to show that the underlying distribution of these labeled categories was actually categorical which brings me down the road of Paul Meehl's work on taxometrics, before I use LTA? I was wondering if there was any growth modeling frameworks that might help get around the above points.
bmuthen posted on Tuesday, January 10, 2006 - 10:13 am
Difficult situation. You can do a longitudinal factor analysis - or growth model - using all the indicators of the 5 factors. But with 56 items that would mean 112 variables already with 2 time points, so that is very heavy. But if you try to first get factor scores, you want to make sure their metric is comparable across time.
How can growth modeling be used to model a multidimensional construct with five dimensions. As far as I understand growth modeling with an outcome variable eg maths scores will vary across time allowing a growth model to be fitted to the data so that one can see the inter and intra individual change. My dependent variable cannot form a composite that makes any theoretical sense so how would growth modeling facilitate this? Over a number of measurement occasions a person may obtain different scores on each subdimension. Since each subscale is independent how can a growth model, model change to show that people change dimensions?
bmuthen posted on Tuesday, January 10, 2006 - 2:57 pm
I was thinking growth modeling where growth is considered for all the 5 latent variable constructs jointly. So 5 correlated, parallel processes.
This is very helpful thank you. I've looked at the mplus user manual on p 89/90 for two parallel processes. If I understand you correctly each dimension will have its indicators/items as well a random slope and intercept. So I will have five random slopes and intercepts per dimension where each dimensions slope will have a double headed arrow going with the next eg s1 covaries with s2 and I1 covaries with I2 S2 covaries with s3 etc and paths would be estimated between each intercept and slope.
If I introduce time invariant covariates ie x then these can be modeled by paths connecting each i and s for each dimension.
Are you familiar with any papers that have used the parallel processing approach?
bmuthen posted on Wednesday, January 11, 2006 - 9:47 am
I can't think of parallel process application papers off hand - others? We discuss them in our courses for which there are handouts.
I would like to get your opinion on a modeling issue on parallel processes. Previous work on this construct used extreme group analysis ie pick highest score on one dimension and ignore the rest of the data for each respondent. If I am modeling the five factors as a parallel process would the raw scores or Z scores be used as data input for all five factors being used in the growth model. I want to avoid the extreme group analysis as I will loose data. Thanks
If growth is considered for all the 5 latent variable constructs jointly with 5 correlated, parallel processes do all five factors appear in the growth model for each time point ie is it a multivariate growth model? So that each five dimensions has an intercept and slope which are connected for all measurement occasions? I'm having a little difficultly in conceptualising a diagram of this from a univariate case?
If you have 5 latent variables at several times points, you would have 5 parallel processes. Each one would have an intercept growth factor and a slope growth factor (for a linear model). Look at Exammple 6.14 which is a multiple indicator growth model for one process. You would have 5 of these and the intecept and slope growth factors of these 5 processes can be covaried or regressed on each other. See Example 6.13 for a parallel process model of observed outcomes. Remember Bengt's caveat. You need to test for measurement invarianceacross time for each of these processes. Our Day 2 short course handout shows the steps in doing a multiple indicator growth model.
If you don't have measurement invariance, then you can't say that the factor is the same at each time point. And if it is not the same construct, studying its development does not make any sense.
I think if you read the paper you will understand what I am saying.
If your outcomes are categorical, you will need numerical integration. The size of your problem would make estimating the model impossible with numerical integration. If you don't have strong floor or ceiling effects in your factor indicators, I would treat them as continuous variables.
Thank you. Can I check this with you? In the multiple indicator growth model. The intercept shows how much of a dimension a person has/demonstrates on each factor per measurement occasion assuming the appropriate loadings on the factor and the other caveats pointed out. The slope shows whether change can be described as linear, or non linear. ie shows that the rate of change may differ per person depending on the variance of the slope parametre and significance of slope coefficient. So with paralell processes there are five intercepts and slopes ,one set per process. By comparing the intercepts across five occasions one can track mean changes from initial stages so that more or less of each factor can be observed across time. By comparing significance of slope coefficients one can see if change is best described by linear quad or polynimial or variants of these across measurement occasions. Thanks for your patience on the matter.
bmuthen posted on Tuesday, January 17, 2006 - 11:03 am
Can mplus run an auxilary threshold model? I am asking because my dependent variable in my growth model is measured using an ordinal variable with 5 points. Hence my level 1 model does not hold for repeated measures relative to a continuous variable. The auxilary regressions connect the ordinal variable to the underlying continuous variable. Rather than just assuming an underlying continuous variable and leaving it at that, I am trying to guage the damage.
In Bollen and Curran 2006 Latent curve models a structural equation perspective p 233-236.
They take a repeated measures approach to a ordinal variable, neighbour satisfaction, and obtain the thresholds for satisfaction with neighbour variable, using lisrel while Mehta et al 2004 9,3 psychological methods pp 301-303 use mx to do a simlar task with a different variable.
Latent variable modeling with ordered categorical outcomes was introduced in the Muthen (1984) Psychometrika article and implemented already in the old LISCOMP program of 1987, so yes, Mplus can do growth modeling with ordered categorical outcomes. Both using WLS and ML. I don't know why the term "auxiliary threshold model" is used in the Bollen-Curran book; that is not standard language for this model. Mplus Web Note #4 gives a description of why I think the LISREL approach is inferior to that of Mplus. With multi-category outcomes that are not very skewed and lack floor or ceiling effects, I would not expect a large difference relative to treating the outcome as continuous.
By floor and ceiling effects do you mean that a lower respose category such as say 1 has a very large proporation of reponses relative to say category 2,3,4 or 5; while a ceiling effect suggests that the highest category eg 5 has the largest proportion of responses.
What constitutes a cut off point for a high ceiling or floor effect? How does one examine data for these effects is it a frequency table?
I'll take a look at the MPLUS webnote and see. Thanks
Given the previous post on Jan 12 2006. It would be best to treat the data as continuous given caveats raised. I assume that the ordinal scale would be treated as an interval scale so that mean, variances and covariances can be estimated within the growth model?
As a side is there anything you can recommend that gives some direction on avoidance of ceilng and floor effects?
If you treat the variable as continuous instead of ordered categorical, means, variances, and covariances are estimated for it rather than thresholds and correlations.
Floor and ceiling effects are a function of what is being measured and how the item is written. People may bunch up because the behavior is very rare or because there aren't sufficient categories to catch the details of the behavior.
On item two,a pilot test is in order prior to modeling.
I have some understanding that thresholds are used to link the ordinal variable with and underlying continuous variable,but if I use ML or some other continuous variable estimation technique, how does the estimation technique reconcile ordinal measurment with a continuous variable assumption to generate a mean, variance and covariance? Or how are these extracted from ordinal data?
I plan to use a 56 item survey with a 5 point likert scale. If this data shows floor and celing effects numerical integration will not work.
My understanding is that if the line items on the likert scale do not exhibit strong floor and ceiling effects I can treat the line items measuring the underlying factor as continuous and apply the growth model instead of trying to estimate a growth model with ordered categorical dep variable.
Hence ,provided I have well behaved data it would be appropriate to treat the survey items as if they were continuous.
This would allow me to use the mean ,variance and covariance instead of having to extract them from a frequency table.
Or have I got the complete wrong end of the stick etirely? Sincere apologies if I have.
I've based the point of numerical integration on the post from Jan 12 Maybe the misunderstanding is on terminology.I'm including ordinal variables as ordered categorical rather than dichotomous and presumed that numerical integration covered ordered categorical as well as dichotomous. Given that your post refers to categorical I took it that the post covered ordinal variables as well and hence the size of my data set would be impossible to work with.
A couple of issues come up here. Variables placed on the CATEGORICAL list in Mplus can be binary or ordinal. The estimation is the same for both.
With categorical outcomes and maximum likelihood estimation, numerical integration is required. With categorical outcomes and weighted least squares estimation, numerical integration is not required. So if you have many ordinal outcomes with floor and ceiling effects, you can use weighted least squares estimation.
I may treat the survey items that measure an underlying factor as continuous provided that there are no strong floor and ceiling effects in the data. I can use ML or MLR( non normal data) to generate a mean variance and covariance in a growth model otherwise select WLS as per previous post for categorical outcome
I suppose the best thing to do is to generate some data with varying degrees of ceiling and floor effects and see what happens eg Muthen and Kaplan paper.
In example diagram of example 6.14 the same intercept and slope look like they are measuring different factors.
Would this not pose a problem of interpretation of slope and intercept if the factors f1-f3 are different? For exampe if f1 stands for past ,f2 stands for future and f3 stands for present. How does the one slope parametre explain change in three different factors or am I missing something?
Example 6.14 is a multiple indicator growth model where development of the factor over time is of interest. Measurement invariance of the factor is required for this model to make sense. Measurement invariance of the factor is reflected by holding the intercepts and factor loadings equal over time.