Anonymous:Specific Question:
In Tuesday’s class, we were given the formula sqrt( ∑∑(Sij-Sijhat)^2/p(p+1)) where i<j to calculate the RMR. Here S is the observed covariance matrix and Shat is the fitted covariance matrix. Then we performed a SAS code to compare RMR and GIF but you said there might be a mistake in that code. After I looked into that code, I got an answer but I don’t know whether it’s right or not. That part of my code is
RMR1 = sqrt(( sum(R1#R1)) +trace(R1#R1) /2*(q1*(q1+1)) ) ;
RMR2 = sqrt( (sum(R2#R2)) +trace(R2#R2) /2*(q2*(q2+1)) ) ;
After run this, RMR1= RMR2=0.3464102.Is this code right?
In Tuesday’s class, we were given the formula sqrt( ∑∑(Sij-Sijhat)^2/p(p+1)) where i<j to calculate the RMR.
It should have been "i<=j". That was the big difference. In the EFA analysis of PROC FACTOR, the diagonals were excluded. Here they are included. Also, it should be divided by p(p+1)/2, not by p(p+1). The way to understand this is that there are p*p total elements in the matrix. p(p+1) = p*p + p is clearly too many. The number of off diagonal elements plus the number of diagonal elements is p(p+1)/2 (just try it for a few cases.)
The code I posted has
RMR1 = sqrt(( sum(R1*R1)) +trace(R1#R1) /2*(q1*(q1+1)) ) ;
not
RMR1 = sqrt(( sum(R1#R1)) +trace(R1#R1) /2*(q1*(q1+1)) ) ;
as you suggest. Why did you change it? You certainly get the wrong answer when you do. Anyway the code is right after all. It sums all the squared elements in the difference matrix, and adds the squared diagonals, So it is twice the sum of the squared diagonals plus off-diagonals. That's why you can divide by p(p+1) instead of p(p+1)/2, which was my concern.
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General Question:
After went trough the article on the web page (Convergent & Discriminant Validity), I am confused about the last part which says that”It does show that, as you predicted, the three self esteem measures seem to reflect the same construct (whatever that might be), the three locus of control measures also seem to reflect the same construct (again, whatever that is) and that the two sets of measures seem to be reflecting two different constructs (whatever they are).” But there is no simple answer to the question “How do we show that our measures are actually measuring self esteem or locus of control?” This article mentions some ideas to address this question, but my general idea has two steps. First, we need to find the correlation matrix of all the Y’s and group them into different measures based on how highly correlated they are and our prior-knowledge to get the construct validity (let’s say 3 measures). Second, we can perform EFA or CFA (if we know there are correlations between the measures) to conform what the measures might be (while, we can not be 100% sure about that). And also, if we cannot conduct a valid construct, then all the following procedures won’t make sense. Is my idea right?
Sounds largely ok, but I don't know what "conduct a valid construct" means, and I don't know what "following procedures" you are referring to.
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