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18

I would go for some papers by Múthen and Múthen, who authored the Mplus software, especially Múthen, B.O. (1984). A general structural equation model with dichotomous, ordered categorical and continuous latent indicators. Psychometrika, 49, 115–132. Muthén, B., du Toit, S.H.C. & Spisic, D. (1997). Robust inference using weighted least squares and ...


17

I would like to answer this question, largely based on the historical perspective, which is quite interesting. Herman Wold, who invented partial least squares (PLS) approach, hasn't started using term PLS (or even mentioning term partial) right away. During the initial period (1966-1969), he referred to this approach as NILES - abbreviation of the term and ...


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 ...


15

Yes, they are very different. Conceptually, a reflective measurement model happens when the indicators of a construct are considered to be caused by that construct. For example, an intelligence test: if you are more intelligent, you have a higher probability of getting the correct answer to a question. Hence your intelligence level is (theorized to) ...


14

My disclaimer: I realize this question has laid dormant for some time, but it seems to be an important one, and one that you intended to elicit multiple responses. I am a Social Psychologist, and from the sounds of it, probably a bit more comfortable with such designs than Henrik (though his concerns about causal interpretations are totally legitimate). ...


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

While only tangent to your goals at this point, if you continue on projects using latent variables I would highly suggest you read Denny Boorsboom's Measuring the Mind. Don't be fooled by the title, it is mainly a detailed essay on the logic of latent variables, and a large critique of classical test theory. I would say it is necessary reading if you are ...


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 ...


11

It appears that this is a model where (almost) everything is regressed on everything else. You have 5 variables in your model. That means you have 10 covariances. You have 10 parameters. The df of the model is equal to (number of covariances) - (number of parameters). This is zero. The model is described as saturated, and it's not testing anything. ...


11

As far as I can tell, Bayesian Networks do not claim to be able to estimate causal effects in non-directed acyclic graphs, whereas SEM does. That's a generalization in favor of SEM... if you believe it. An example of this might be measuring cognitive decline among people where cognition is a latent effect estimated using a survey instrument like 3MSE, but ...


10

You must have uncovered a bug in polycor, which you would want to report to the John Fox. Everything runs fine in Stata using my polychoric package: . polychoric * Polychoric correlation matrix A1 A2 A3 A4 A5 B1 B2 B3 C1 D1 E1 A1 1 ...


10

Simultaneous Equation Models (let's call them SIM to separate the two types of models), are models where you have some simultaneity. For example, $$ y=\alpha+\beta x + u_y\\ x=\gamma+\delta y + u_x $$ As you can see, the two equations form a system of equations. These are widely used in econometrics and applied economics, but it is not guaranteed that they ...


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 ...


10

There is a nicely written and highly-cited chapter by Finney & DiStefano (2008) that speaks to your questions (you can view most of it on Google Books). In summary, multivariate normality is typically evaluated using univariate skewness and kurtosis, and multivariate kurtosis--values less than 2, 7 and 3, respectively, are generally considered acceptable,...


9

I built on @Andy W's R-code and hope my changes are useful to someone else. I mainly changed it, so that it obeys the new syntax (no more opts) in ggplot2, so no more warnings adds the correlations as text now correlation text size reflects its effect size colour scheme shows the type of correlation (hetero/mono-trait/method). put the legend in the empty ...


9

I don't think the currently accepted answer is correct. What it describes is identification, not standardization. The unstandardized coefficients is what comes directly out of the estimation procedure. The standardized coefficients recast regression coefficients and covariance in metrics of correlations, and unique variances, in terms of $R^2$. So if you ...


9

There isn't currently a method implemented at the model level, but you can create a new variable that is just attitude1*group, or you can just use multigroup analysis, which may be more appropriate in this case.


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

They're the same model. It's useful to be able to define a latent variable as a composite outcome where that variable only has composite indicators. If you don't have: f1 =~ y1 + y2 + y3 You can't put: f1 ~ x1 + x2 + x3 But you can have: f1 <~ x1 + x2 + x3


9

It is possible to do EFA in a CFA framework. This is sometimes called "E/CFA". A nice discussion of this can be found in: Brown, T. A. (2006). Confirmatory factor analysis for applied research. New York: Guilford Press. For this to work, you need to have an "anchor item" for each factor, for which there are no cross-loadings. Looking at the results from ...


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

Your model is saturated. You have 6 covariance moments (three variances and three covariances), and you are estimating 6 parameters (factor variance, two loadings, three measurement error/unique variances). The problem has an exact solution, and zero objective function means that Amos successfully found that solution. It also means that you cannot use the ...


8

Baron and Kenny are indeed outdated, though that does not make them wrong in all cases. The concerns divide into broadly statistical limitations and assumptions which are discussed in the reference your reviewer suggests and in the literature alluded to by @PeterFlom, and broadly non-statistical concerns about the definition and causal identification of ...


8

If negative values are impossible for these features, you should impose a constraint/prior on the imputation procedure. The Amelia II documentation provides extensive explanation of how to go about this from many different angles. You can impose a boundary, or a prior with most of is mass far from the boundary, or transform the data, or... To answer your ...


8

Many statistical tests can be thought of as structural equation models, and one of those is the paired samples t-test. As you say, the advantage of the SEM approach is that you can use FIML estimation - which is asymptotically equivalent to multiple imputation, but can be easier. You estimate a parameter which represents the difference between the means, ...


8

As Maarten points out, your problem is that you have not set the scale of the second model. True, you have more observed variances/covariances than what you need to identify your model, but you still need to provide a point of reference from which other model parameters can be calculated (Brown, 2015). You can set the scale using one of three methods: ...


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 ...


8

You are not missing anything, the correct answer is $-9500$! First find the idiosyncratic characteristics of Caroline, by updating her background variables $U$ given the evidence $EX = 9$, $ED = 2$, $S = 97000$. This is the Abduction step, $$ 97000 = 65000 + 2500(9) + 5000(2) +U_{s} \implies U_s = -500\\ 9 = 10-4(2) + U_{EX} \implies U_{EX} = 7 $$ Now we ...


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