32

Your approach to testing mediation appears to conform to the "causal steps approach" described in the classic methods paper by Baron & Kenny (1986). This approach to mediation entails the following steps: Test whether X and Y are significantly associated (the c path); if they are not, stop the analysis; if they are... Test whether X and M are ...


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. ...


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

The first question is what is the difference between "PLS path modeling" and "PLS regression"? None, they are synonyms. To make it more general, what are structural equation modeling (SEM), path modeling and regression? To my understanding regression focuses more on prediction while SEM focus is on the relationship between response and predictors and ...


6

e1, e2, and e3 are not parameters, these are error terms in the path model. You may need to clarify your understanding of path notation (and may be structural equation modeling in general). These variables do need their parameters, the variances -- I will refer to them as $\psi_k, k=1, 2, 3$. You would also need the variance of x1 as the model parameter; I ...


6

Your model is not identified. That means that Lavaan cannot find a unique solution, and cannot compute standard errors. Because it can't find a unique solution, it's finishing in different places. [Very simple example of identification: $x + y = 5$ There are many (an infinite number) of solutions to this equation for x and y, and they're all equally good, ...


5

The Lasso is the solution to $$\hat{\beta} \in argmin_\beta \frac{1}{2n}\Vert y-X\beta\Vert_2^2 + \lambda\Vert\beta\Vert_1$$ Evidently, $\hat{\beta}$ also depends on $\lambda$, so really, we could write this dependence explicitly: $\hat{\beta}(\lambda)$. Thus, we can interpret $\hat{\beta}$ as a function $\lambda\mapsto\hat{\beta}(\lambda)$, whose domain ...


4

If your model is complicated, I would recommend xxM, a package for R by Paras Mehta. http://xxm.times.uh.edu/ Mehta, P. D. (2013). n-level structural equation modeling. In Y. Petscher, C. Schatschneider & D. L. Compton (Eds.), Applied quantitative analysis in the social sciences (pp. 329-362). New York: Routledge.


4

In regards to the ability to pull this off in any SEM program....yes, you don't always need specialized SEM software, but you might have a hell of a data wrangling job if you don't use SEM software that is specialized for this task. FYI: I don't find openmx to be intuitive. Here's a reference for pulling this off in most any software, which wasn't ...


4

Panel models are quite common in longitudinal SEM. It sounds like might be new to this approach to data analysis, so I would suggest Little (2013), which will give you good coverage of the basics of SEM, as well as an intro to panel models, specifically (and I'm sure many of the references throughout that chapter will be useful to you as more detail-oriented ...


3

I think I know the answer to my question. I tried a few models like the ones shown above, using the sample data sets from lavaan in R. Typically, models that simply replace a two-headed arrow (correlation) with a one-way arrow (regression) have the same number of degrees of freedom and cannot be distinguished from each other. A model like $X \rightarrow Y \...


3

As far as I know, no SEM software (including AMOS, Lisrel, the sem and lavaan packages, or Mplus) currently will do this and that's a good thing. For a given model, there are equivalent models that have equally good fit (e.g., Stelzl, 1986; Lee & Hershberger, 1990; MacCallum et al., 1993). See also: http://www2.gsu.edu/~mkteer/equival.html Therefore, ...


3

Not free, but this introduction is a great value at $16: James Davis' The Logic of Causal Order (Sage pubs.) See reviews.


3

Your estimated model looks like: \begin{align} \sqrt{V_2} &= a_2 \left( 1+V_1 \right)^{b_2} + \epsilon_2 \\ \sqrt{V_3} &= a_3 \left( 1+V_2 \right)^{b_3} + \epsilon_3 \\ \ln{\left(1+V_4\right)} &= a_4 + b_4 V_2 + c_4 V_3 + \epsilon_4 \\ \end{align} What you are interested in calculating is $\frac{d V_4}{d V_1}$. To do this, we are just going to ...


3

I presume you mean to ask which direction should you attempt in order to get to 2 in the smallest expected number of moves--you'll reach the finish with probability 1 eventually. You have to get to the square to the left of 2. So what's the better way to get to that square, going right twice and then up twice or up twice and then right twice? Both paths are ...


3

Let the variables be stardadized to unit variance and let's use $\sigma_{ab}$ to denote the covariance of $A$ and $B$. You want the correlation of $A$ and $C$ when conditioning on the collider $B$. Thus, you can write the partial correlation $A$ and $C$ given $B$ as: $$ \rho_{ac.b} = \frac{\sigma_{ac} - \sigma_{ab}\sigma_{bc}}{\sqrt{1 - \sigma_{ab}^2} \...


2

The required sample size depends on the size of the model. You said you have 5 latent variables, but how many equations do you have? How many indicators are measuring the latent variables? In general: The bigger you model, the larger your sample should be. There are no commonly accepted minimum sample size criteria, only rule of thumbs. As for my opinion I ...


2

Wow. 120 items is a lot. Are they yes/no (0/1)? Do you just use a simple sum? You could try approaching this with fixed reliabilities of your factors. Compute your scores and store them as say f1score through f5score. In AMOS, specify latent variables as circles with f1 through f5 in them, and connect them to the rest of the model. Now, connect each of the ...


2

Just as null hypothesis significance tests ("sig. or non-sig.?") have been widely criticized for answering a question that interests few people, the use of a cutoff in assessing reliability is not generally very helpful. It's better to treat reliability as something that's measured on a scale. And note that, yes, for some contexts 0.7 is highly ...


2

A multiple regression model is a special case of a path model. There are many analyses that can be conducted via path models. Only some of those can be fit with multiple regression models. If a multiple regression model is a viable option, either could be used. In that case I (and I suspect most data analysts), would use a standard multiple regression ...


2

I think the author of that link is being a bit severe. The default, in structural equation modeling, is for residual variances to be uncorrelated, but you can posit correlations between them if you think it makes sense to do so. However, residual correlations will weaken the wow factor of your model. Presumably, you are saying that math at age 6 is related ...


2

Although as far as I can tell the 3rd edition of Schumacker & Lomax doesn't answer my question, the 4th edition (from 2015) does! Quoting p84 of that text (but changing the figure to match my data), the answer to the question is: "The $R^2m$ for the path model would suggest that [32%] of the variance in [timedrs] is explained by the relations in the ...


2

The solution using the mcglm package. Extra packages require(mvtnorm) require(mcglm) require(Matrix) Simulating the data set set.seed(13092016) Covariates env1 <- rnorm(100) env2 <- rnorm(100) Trait 1 par1 <- 5 par2 <- 2 var1 <- 0.5 mean1 <- par1*env1 + par2*env2 Trait 2 par3 = -1 par4 = 3 var2 = 1 mean2 <- par3*env1 + par4*...


2

It is a bit tough to discern what is going on without looking at the actual paper, but that appears to be from a Path Analysis or Structural Equation Model, where parameters are estimated for direct and indirect effects of variables on one-another. I tried to find the paper via google scholar, and while I don't have access to the journal, I saw in the ...


2

Welcome to CrossValidated. RMSEA is a measure of approximate fit - if it's below a certain value, the fit is considered OK. Trouble is, it's a sample statistic, like the mean, and we'd like to know about the population parameter, not the sample statistic. In a regular null hypothesis test, we're usually trying to test against zero - zero means no effect. ...


2

I think (c). Allowing the outcomes to covary is appropriate. If you don't, the model is wrong (and you'd see this in the fit statistics). Your results should (very close to) exactly the same as if you did a multivariate regression - which isn't a surprise, as you fitted the same model. (And by results I mean estimates, standard errors, CIs, etc).


1

Based only on this error is difficult to figure out what is going on. This is the unique error possible to occur when using mcglm. It is just telling you that the variance-covariance matrix is not positive definite. Assuming, that your model is correct specified and you data support your model, if you control the step-length through the tunning argument it ...


1

It's important to distinguish causal or conceptual assumptions from statistical assumptions here. Reverse causality, for instance, has no test, since statistically $A \rightarrow B$ leads to a probability model for $P(A, B)$ that is identical to $B \rightarrow A$ without control for additional causal moderators. Unlike most regression techniques, SEM ...


1

I agree with the jsakaluk's answer, and I would like to add more relevant information. Baron and Kenny's (1986) method of testing mediation has been extensively applied, but there are many papers discussing severe limitations of this approach, which broadly include: 1) Not directly testing the significance of an indirect effect 2) Low statistical power ...


1

As @wolfgang says, it's a good thing that this is very difficult. Kind of the point of SEM is that you start with a specified model, and then you test it, and use the chi-square (and other fit statistics) to decide if you have a good fit. IN a chapter called "Testing structural equation models" Joreskog talks about this as the 'strictly confirmatory' ...


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