Thank you. Yes I understand that the standard error is automatically provided by any software. However I want to know how it was calculated.

Dear Prof. Dijkstra,

I used a WLS estimator instead of ML due to the high sknewness and kurtosis of my data. Thank you very much for a very detailed comment. I was able to be more clear on how the standard error being derived. However, I will need to read more in order to understand deeply this issue.

The note you provided was very helpful. In addition to this note, could you please spend a moment with writing another note on the relation between information matrix and curvature? I believe this would benefit many other students.

Also, could you please explain the meaning of "standard error"?

Wish you a good health!

Best regards,

Tran Viet Yen.

Dear Prof. Dijkstra

Thank you very much for the explanation. Yes that is the reason why it is used to calculate the t-values for examining the significance of factor loadings.

Thank you in advance for the future note. Please post it at any time when it is available. I highly apprecite your time.

Best regards,

Tran Viet Yen.

Dear Prof. Dijkstra

Thank you very much for the explanation on the relation between the curvature of L and the reciprocal of Fisher’s information. I highly appreciate your valuable time spending on this issue and your kindness also. It took me quite much time to get an insight into your script, hence replying you late.

On this point, I would like to ask you the follow-up.

My understanding is:

- The curvature of L (at the theta-hat) = (1/r) = E (the Fisher information matrix), while r is the radius of the circle;

- The variance of theta-hat = (approximately) r = the inverse of E (as demonstrated above) -> take square root of the variance (in this case, E) we get the standard error: (1/sqrt(E))

(It also means that the standard error is defined as the square root of the corresponding diagonal element of the inverse of the Fisher’s information matrix.)

On this point, could you please explain the meaning of the variance of theta-hat, which take the value of r by the large-sample-theory? You mentioned that “theta_hat is approximately normally distributed around the true theta, with a variance approximately given by the reciprocal of Fisher's information, so just r.” I think theta_hat is not a variable, but just a value which satisfies that at theta-hat, the log likelihood function is maximized. So what is the meaning of “variance of theta-hat”.

Secondly, you mentioned that in order to satisfy the standard-large-theory above regarding the variance of theta-hat, the density we use in the log likelihood function is “true density”. If the data is non-normal, the ML estimator can still be used providing that we know the true density. But how do we know the “true density” from just a sample data obtained? Also, as you mentioned, we need to adjust the Fisher matrix when calculating the variance of theta-hat to account for the fact that the data is non-normal. In that case, it seems the existing SEM softwares are unusable.

Once again, thank you very much for your explanations and the references.

Best regards,

Tran Viet Yen.

Dear Prof. Dijkstra

The explanation is very helpful. I was made clear on the meaning of the standard error and how the model is test for significance. I will certainly read these books for futher understandings.

Thank you very much and wish you a good health!

Best regards,

Tran Viet Yen.

Dear Prof. Dijkstra

Thank you very much for giving proof for the determination of the variance of estimator - the curvature of the L(theta) spiral - the Fisher information matrix. It is really helpful and informative.

Best regards,

Tran Viet Yen.