17

In some ways you are right, CFA and IRT are cut from the same cloth. But it many ways they are quite different as well. CFA, or more appropriately item CFA, is an adaption of the structural equation/covariance modeling framework to account for a specific type of covariation between categorical items. IRT is more directly about modeling categorical variable ...


16

SEM is an umbrella term. CFA is the measurement part of SEM, which shows relationships between latent variables and their indicators. The other part is the structural component, or the path model, which shows how the variables of interest (often latent variables) are related. You can run CFA alone, path analysis alone, or a full SEM. Path analysis is SEM ...


14

1. Go back to Exploratory Factor Analysis If you're getting very bad CFA fits, then it's often a sign that you have jumped too quickly to CFA. You should go back to exploratory factor analysis to learn about the structure of your test. If you have a large sample (in your case you don't), then you can split your sample to have an exploratory and a ...


13

1) The baseline is a null model, typically in which all of your observed variables are constrained to covary with no other variables (put another way, the covariances are fixed to 0)--just individual variances are estimated. This is what is often taken as a 'reasonable' worst-possible fitting model, against which your fitted model is compared in order to ...


12

A CFA is pretty easy to do in R with OpenMx, sem, or lavaan. Since a CFA is such a vanilla case of SEM, all three are pretty easy to implement and offer helpful walkthroughs within their respective documentations. I personally use OpenMx or lavaan. One thing to keep in mind if you use OpenMx is that it won't give you fit statistics by default, you have to ...


10

Because it then allows you to use the relationship between the latent variable and the observed variable to determine the variance of the latent variable. For example, consider the regression of Y on X. If I am allowed to change the variance of X, say, by multiplying it by a constant, then I can change the regression coefficient arbitrarily. If instead I ...


10

The point of running an structural equation model is to be able to be wrong - and that's only true if it's over-identified (i.e. has degrees of freedom greater than zero). You can specify a multiple regression model as a structural equation model, you'll get the same answer, and the model will be just identified, so it will have zero degrees of freedom. But ...


9

That's pretty normal. CFA is a much more stringent criterion than EFA. EFA attempts to describe your data, but CFA tests if the model is correct. One reason for non-convergence is low average correlations (but then I'd expect RMSEA to be better). The chi-square test is essentially a test that your residuals are equal to zero, and RMSEA, TLI and CFI are ...


9

The covariance matrix of the data is always non-negative definite, there is no doubt about that. However, the model-implied covariance matrix may not be when some parameters take values outside their natural ranges. In turn, this may happen for a number of reasons. Your 4-factor model may be misspecified, i.e., does not fit the data right. Your model is OK,...


9

The source of your problem is the 'robust' estimation of standard errors using the robust Satorra-Bentler Chi-square statistic. When testing for measurement invariance, we compare less constrained (configural invariance) to more constrained (metric or scalar invariance) models. The comparison that is usually applied is a Chi-square difference test, which ...


8

Model A is nested in model B if some of the coefficients in B, or their combinations, can be restricted to obtain model A. In case of CFA models, the number of factors is a moderately complicated example of nesting. Consider a two-factor model (taken from UCLA ATS website) A simpler one-factor model will be nested in it with a linear constraint $${\rm ...


8

It is generally a bad idea to do an EFA and a CFA on the same data for the exact reason you mention: A factor structure derived from an EFA will almost always fit very well in a CFA using the same data. EFA and CFA are closely related, so it is no surprise that this is the case. It is common to split data in half and to do EFA on one half and CFA on the ...


8

The intercept or mean of a latent variable is arbitrary, like the variance, and is usually fixed to zero if you have a single group model (or a single time point model). The intercept of the measured variable is the expected value when the predictor (the latent variable) is equal to zero. You anchor the mean of the latent variable to the intercept of the ...


7

I may be misunderstanding the phrase "indeterminancy of scale", but I believe it is set to one for identifiability. (That is, the number of unknowns in this system of equations should not exceed the number of equations.) Without setting one of the links to one, there are too many unknowns. Is that the same thing as indeterminancy of scale? In most SEM ...


7

@Philchalmers answer is on point, and if you want a reference from one of the leaders in the field, Muthen (creator of Mplus), here you go: (Edited to include direct quote) An MPlus user asks: I am trying to describe and illustrate current similarities and differences between binary CFA and IRT for my thesis. The default estimation method in Mplus ...


6

You can calculate the reliability of your items from the CFA. From your standardized solution, calculate: (L1+...Lk)*2/[(L1+...Lk)*2+(Var(E1)+...+Var(Ek))] This will give the composite reliability, which should be close to alpha. It's harder to have good fit if you have high alpha, and it's harder to have high alpha if you have good fit. The extreme ...


6

Basic SEM attempts to explain variance in measured variables through predictive relationships with a latent variable. In a simple, single common factor model, one latent factor is estimated as a potential explanation for all common variance in a set of related measurements. In a typical case of strongly correlated measurements, each measurement will ...


6

A CFI of 0.9 is generally considered to not be very good (nowadays?). So saying that a CFI that is below 0.9 is "almost a good fit" is (IMHO) stretching the truth somewhat. So why do you have good RMSEA and poor CFI? It's because the two indices test fit in different ways. RMSEA is based on chi-square - lower chi-square means lower RMSEA. The CFI tests fit ...


5

The "1" means that the coefficient for that particular path has been set (fixed) to 1, as mentioned by Peter Flom. The diagram you refer to is reproduced here: In order for a latent variable to have a scale either its variance must be fixed (often to 1), or a path to one of it's indicators must be fixed (usually to 1), as in this case. The same applies for ...


5

Ordered categorical items and normality: First, ordered categorical items are discrete and lumpy. In particular, 3-point response scales lack the granularity required to even provide a rudimentary approximation of normality. When you have more response options in your ordered categorical variable, the item has more potential to approximate a normally ...


5

$df = moments - parameters$ You've got 10 parameters to estimate in the $\lambda$ matrix in the EFA, and only 5 parameters in the $\lambda$ matrix in the CFA because constraints are added in the CFA. Hence you have more df in the CFA. You can't free all of the parameters in the lambda matrix in CFA, because you will end up with negative df. This is the ...


5

I believe you should do the structural equation modeling on the second half of the dataset. As you say in your question, the basic process is: You split the dataset, and the first half you do the EFA on. This is where you explore the data and get a feel for how the structure shapes up. But who knows if this is just due to artifacts of the data you had? So ...


4

Generally, you should remove the item and use the remaining items to estimate your latent variable in the measurement model. Items with no variance add no information and will make the correlation matrix blow up. You can get prune them using something like this: library(psych) descriptives <- describe(data) good_variables <- which(descriptives$range ...


4

@Richiemorrisroe has provided a concise answer, but here's a little elaboration. In CFA you choose to permit factors to correlate (e.g., in path diagrams by adding double headed arrows between factors). Part of interpreting the model involves examining the relative size of correlation between factors. It sounds like you were expecting all the factors to ...


4

Think about the interpretation as if it were just a simple regression. The coefficient reflects the unit difference in the dependent variable associated with a 1 unit difference in the independent variable. Thus if a 1 unit change in in the IV is associated with a 1 unit change in the DV, then the units are funcationally equivalent. You need a unit for the ...


4

Main Point With only two observed variables per factor, the latent variable can not generally be estimated. Having correlations between factors presumably adds enough constraints to the model to allow estimation of the latent factors, but without those correlations, the latent factors are not estimatable. What should you do? Add more observed variables ...


4

There are a lot of implicit questions in here, it's not absolutely clear to me what you're asking. However, there's one explicit question: "What should I do if respondents are answering everything in STRONGLY AGREE or AGREE?" This is a problem with the data, not with the analysis. You don't have information differentiating people (or you have very little). ...


4

I would work on trying to get the bifactor model to converge. Try adjusting the starting values...this may be a fishy approach though, so bear that in mind and interpret with caution. Read up on the dangers of interpreting models that resist convergence if you want to be truly cautious – I admit I haven't done this much yet myself in my study of SEM, so I ...


4

There are two questions here: (1) do you need to fit/examine a measurement model before fitting/examining a structural model? and (2) if a given measurement model exhibits poor fit, is it still worth fitting/examining a structural model. This is essentially a matter of could v. should. Could you just skip to fitting a structural model? Yes. Should you? ...


4

The thresholds are on a logit scale, so it's the log-odds (just like in logistic regression, or ordinal logistic regression). The thresholds are just like the intercept in a regular regression model. They give the expected log odds of a value, given that the predictors (including latents) are equal to zero. If in a model with continuous variables, you ...


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