Anonymous:
1. Model test
The structural equation model is composed of measurement model and the structure among constructs. Suppose the following model with F1 and F2 are constructs measured with Y1, Y2, and Y3, Y4 and Y5 indicators respectively. Also, F1 and F2 affect to F3, and subsequently F3 affects F4.
Y1 <- F1 -----
Y2 <- ---> F3 --> F4
Y3 <- --
----
Y4 <- F2 ----
Y5 <-
When testing this model with a survey, we usually put the questions that are only considered between two constructs at a time, questions like F1toF3, F2toF3, and F3toF4. I think this test has a problem because the test assumes that if F1toF3 and F2toF3 are true, F3toF4 is true. We do not know F1 affects F4, and then F3. Thus, why we do not make a question about this like “I think F1 and F2 affect F3, then subsequently F4. 1 2 3 4 5 6 7 (7 Likerts)”
Also, if we assume that latent variables such as satisfaction are exist, why don’t we ask about latent variables to respondents directly, rather than making indicator questions and drawing latent variables based on them? Because respondents also understand what satisfaction is, I think it is better to ask latent variable directly. Sometimes, we can feel that researchers treat respondent inferior when taking questionnaires. Generally most of constructs are rephrasing same contents or contexts. So we can know what a researcher asks although there are many items. If so, why researchers ask questions with difficulty leaving out easy question?
You said "Thus, why we do not make a question about this like “I think F1 and F2 affect F3, then subsequently F4. 1 2 3 4 5 6 7 (7 Likerts)”
Do you mean you want to ask the people answering the survey what they think the model should be? This is strange. They are not even aware if any F's or any model. They are just filling out the survey.
You said,
"So we can know what a researcher asks although there are many items. If so, why researchers ask questions with difficulty leaving out easy question?"
Good point! The answer to your question (rephrased), "Why not just ask a single question directly, rather than mulitple indirect questions" lies in the accepted theory is that the "truth" is multifaceted, and that people will not answer a question like "are you satisfied" very reliably. On the other hand, through asking a battery of questions that tap into various multifaceted aspects of "satisfaction," the accepted theory states that the resulting summate will be a more reliable measure. At least, that's the accepted theory. It's not necessarily true, but it is the accepted theory.
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2. Too many model fit indices
In the regression analysis, we need relatively few of model fit indices such as t-test and F-test. However, in the structural equation model, we can see a lot of model fit indices, usually occupied one page in the SAS output. Although fit indices usually measure the difference between observed data and estimated data, why SEM requires a lot of fit indices? If we can apply the five assumptions in the regression analysis to the SEM, is it enough with only just few tests such as t-test and F-test? Also why SEM fit indices have no single statistical test of significance that identifies a correct model given the sample data? I can conjecture two reasons for many model fit indices. One is that SEM is more complicate than the regression model. However, the complexity of SEM could not be a reason because the regression model also can have very complicate model. Next, small sample, violation of normality and independence, and estimation methods can affect the number of fit indices. However, these restrictions are also limited to the regression analysis.
You said,
"In the regression analysis, we need relatively few of model fit indices such as t-test and F-test."
This is not true - we look at lots of tests for adequacy of the model fit in regression. We test linearity, constant variance, independence and normality, in addition to obtaining the Rsquare measure for strength of relationship. The goodness of fit indices in SEM are more similar to all those tests for regression model adequacy than they are to the Rsquare and t tests. We also have Rsquare and t test measures in SEM, and these are more directly comparable to the regression Rsquare and t tests.
Viewed in this way, the reality is that SEM users typically evaluate MANY FEWER fit measures than do regression analysts. The SEM users are simply willing to assume linearity, homoscedasticity, independence, and often even normality. Regression analysts tend to be much more careful and worry about these assumptions. The SEM users might think they are doing a more complete job because they are looking at so many fit measures, but in reality, all the fit measures are doing one thing, and one thing only: comparing two covariance matrices.
You said,
"Although fit indices usually measure the difference between observed data and estimated data..."
Careful - that's not true. They compare covariance matrices, not actual data.
"If we can apply the five assumptions in the regression analysis to the SEM, is it enough with only just few tests such as t-test and F-test? "
See above -we have many other tests in regression for these assumptions. Also, SEMmers are typically willing to ignore all the assumptions.
"Also why SEM fit indices have no single statistical test of significance that identifies a correct model given the sample data? "
You are asking for too much. Such a statistic does not exist for ANY statistical model! You can never find the true model, ever. It doesn't matter whether we are talking regression, SEM, ARIMA, MANOVA, MANCOVA, or whatever else. I hope you didn't *really* such a statistic existed, did you? (If so, I completely failed as a teacher!)
As far as "many fit indices in SEM", again, there really is only one concept here: difference between two matrices. It is simply packaged in many different ways, given the appearance of many things to check. In reality, SEMmers check far *fewer* assumptions than do regression analysts. SEMmers are simply willing, blindly, to assume not only that all regression assumptions are true, but also that the latent variables that they purport to measure actually exist.
It's actually quite amusingly ironic that there are so many SEM fit indices, when in reality SEMmers do so little assumption checking.
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