In article <[EMAIL PROTECTED]>,
Mobile Survey <[EMAIL PROTECTED]> wrote:
>First of all I thank everyone here for their prompt responses.
>[EMAIL PROTECTED] (Herman Rubin) wrote in message
>news:<a604p8$[EMAIL PROTECTED]>...
>> Non-normality will cause problems with classical testing,
>> but that is questionable in any case.
>But would not using GLS help me get over this? I cannot use MLE
>because I have a fairly big sample size (more than 300)and I
>understand that MLE is extremely sensitive for sample sizes above 200.
I can see no reason why MLE should be sensitive to large
sample sizes; if the model is even fairly close to correct,
the larger the sample the better. GLS is essentially a
version of MLE, anyhow. However, if the model is even
slightly wrong, be prepared to find it rejected for large
samples. This does not mean it should be discarded; the
real question is whether it is close enough that it should
be used.
>> If one uses a loading-normalized model with covariances,
>> not correlations, then the asymptotic distribution of
>> the difference between the estimated covariance matrix
>> of the factors and the actual sample matrix, and the
>> estimated specific variances and the sample values, is
>> largely independent of anything.
>Cant I do this using AMOS? Also, could you kindly suggest a reference
>for this
I have no idea what AMOS is.
AFAIK, this appears in an abstract of mine in the _Annals
of Mathematical Statistics_, 1955. If you are familiar
with the use of the "delta method" to get asymptotic
results, it should not be difficult to produce the proof.
The idea is this, where X_i is the observation vector
for the i-th case, F_i the factor vector, and S_i the
specific factor vector. The model is
X_i = L*F_i + S_i.
Then the sample covariance matrix satisfies
M_XX = L*M_FF*L' + L*M_FS + M_SF*L + M_SS.
If M_FS and the off-diagonal elements of M_SS were to be
exactly 0, the MLE of L, M_FF, and the specific covariance
matrix would be the actual values of L, M_FF, and M_SS.
If the usual independence assumptions are made, and
these can be weakened to somewhat more than lack of
covariance, sqrt(n)*M_FS and sqrt(n)*(M_SS - diag(M_SS))
are asymptotically normal, and one can then expand the
logarithm of the likelihood function to obtain the errors
as approximately jointly normal multiples of 1/sqrt(n).
--
This address is for information only. I do not claim that these views
are those of the Statistics Department or of Purdue University.
Herman Rubin, Dept. of Statistics, Purdue Univ., West Lafayette IN47907-1399
[EMAIL PROTECTED] Phone: (765)494-6054 FAX: (765)494-0558
.
.
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