Comments and answers for "Different variances in SPSS and AMOS for the same latent variable"
https://developer.ibm.com/answers/questions/356098/different-variances-in-spss-and-amos-for-the-same.html
The latest comments and answers for the question "Different variances in SPSS and AMOS for the same latent variable"Answer by memic
https://developer.ibm.com/answers/answers/357937/view.html
@Bettina Weber and @mntwz Thank you both for your very helpful responses!
I understand that the imputed latent variable is indeed somewhat different from the latent variable in my model, but now I see the reason.
I am very grateful for your help. Thanks!
M.Tue, 21 Feb 2017 06:54:15 GMTmemicAnswer by BettinaW
https://developer.ibm.com/answers/answers/357724/view.html
@mntwz Thank you for your answer as well!
@memic
This is the reply from AMOS development:
Question about AMOS CFA regression imputation:
1. Use the factor score weights (multiplied by the variables) to get the latent variable in the dataset is feasible. However, the original syntax from M needs to be modified to centralize the variables:
“Compute LAT_fs=(v5-75.432900)*0.00687836046300124+(v4-80.411255)*0.00940926244280345+(v3-64.204545)*0.0116608909933018+(v2-68.885281)*0.00934220602920611+(v1-74.437229)*0.00799622307773429.”
This way the mean and variance of the calculated latent variable is consistent with imputed variable from regression imputation.
2. Regression imputation for CFA model will use the factor score weights as regression coefficients to impute the latent variable. In other words, the regression imputation results should be exactly the same as what we get from running the syntax. Since the regression model does not consider the error term, the variance of the estimated latent variable is not exactly 1 (0.861 in this case).Mon, 20 Feb 2017 08:05:24 GMTBettinaWAnswer by mntwz
https://developer.ibm.com/answers/answers/357446/view.html
Bettina’s answer sounds correct to me. I don’t have anything to add to it except to report a calculation I did to confirm her explanation. I took the “All implied moments” output from your Amos output and reformatted it for input to Statistics. That .sav file is attached to this posting. It contains implied means, correlations and standard deviations for the six variables in your model (not counting the error variables). Then I used statistics to predict the latent variable using the five measured variables as predictors. My syntax was
REGRESSION MATRIX = IN('c:\garb\ImpliedForAll.sav') /VARIABLES=LAT v1 v2 v3 v4 v5 /DEP=LAT /METHOD=ENTER.
In the regression output Statistics reported an R-square of .858. So if the variance of the dependent variable (LAT) is 1, then the variance of the predictions would be .858 and the variance of the errors would be 1-.858=.142.
This is a pretty close match to the variance of .861 that Statistics reported for the imputed scores on LAT. I’m not sure whether one should expect an exact match between the two ways of estimating the variance of the predictions. For what it is worth, the .861 obtained from the imputed scores is an unbiased estimate (divide by 307) and if you use the biased estimate (divide by 308) you get an even closer match to .858.
[link text][1]
[1]: /answers/storage/temp/13109-impliedforall.zipFri, 17 Feb 2017 14:01:44 GMTmntwzAnswer by BettinaW
https://developer.ibm.com/answers/answers/357043/view.html
@memic
Thank you for the files! I have provided your comment and your files to my contact and I hope he can look at it. Please note that I may not have an answer tomorrow, please wait a bit, thanksThu, 16 Feb 2017 09:52:03 GMTBettinaWAnswer by memic
https://developer.ibm.com/answers/answers/357034/view.html
@Bettina Weber, thanks for the answer.
I think we need the model and the data file, because otherwise I have the impression that I would draw a wrong conclusion:
The way I understand it at the moment is: I would assume that Amos (when using regression imputation) internally changes the direction of my arrows towards the latent variable. This would mean that AMOS imputes a variable completely different from the interpretation based on my CFA model and latent variables (fully missing) cannot be imputed. Would this not raise doubts on any model based imputation, even if there were no latent variables but only missing values in some variables? Besides also, when I use Bayesian or Stochastic regression imputation, the variance of the imputed latent variable (computed with SPSS) does not match the variance shown in the output of AMOS.
Another way to get the latent variable in the dataset, is to use the factor score weights (multiplied by the variables). This way I get also a variance far from one, i.e. nearly the same variance like SPSS is showing for the imputed variable (maybe this is due to rounding), but now the mean of the variable is not zero (at least their Pearson Correlation is one).
Why are these variables so different from what to expect? What did I do wrong?
I’m attaching [here][1]:
- the model,
- the data file (RAW) and also
- a data file (RAW_C) containing two more variables: the regression-imputed
latent variable and the variable,
computed through factor score weights
and
- a SPSS-Syntax file with the command regarding the factor score
weights
Thank you for helping me thinking about this!
M.
[1]: /answers/storage/temp/13067-latent.zipThu, 16 Feb 2017 09:09:27 GMTmemicAnswer by BettinaW
https://developer.ibm.com/answers/answers/356778/view.html
@memic
I got this reply:
"The regression imputation method in Amos impute the missing value in latent variable by building a linear regression model with latent as target and other variables as predictors, then using the observed values of predictors to predict the latent, these predicted value will be imputed in the missing of latent variable. I think the CFA and missing imputation are two independent algorithms so you get the different variances. Since I did not see your data and CFA model, that is just my guess."
is this enough answer for you? If not we may need your files attached here, the AMOS model and the data file,
thanks.Wed, 15 Feb 2017 13:39:34 GMTBettinaWAnswer by memic
https://developer.ibm.com/answers/answers/356704/view.html
Thanks! Maybe this finding could shed some light on this problem:
I found out that this problem could be due to the in AMOS implemented method of "regression imputation":
Maybe the imputed latent variable cannot be the latent variable itself, but it is only a ML-estimation of it with a variance that is as similar as possible to the real latent variance, because the model is first fitted using maximum likelihood (ML) and only after that the restrictions (e.g. latent mean = 0, latent variance = 1) are set to their ML estimates. (see Arbuckle, 2014 "IBM SPSS Amos 23 User's Guide" p.463)
Could this be the reason?
If so, is it in any way possible to set the restrictions before fitting the model or does it makes no sense?
M.Wed, 15 Feb 2017 08:36:14 GMTmemicAnswer by BettinaW
https://developer.ibm.com/answers/answers/356423/view.html
@memic
sorry I cannot answer this question. Maybe I will find someone who can, but cannot guarantee. If I have something I post it here.
regards
BettinaTue, 14 Feb 2017 11:51:00 GMTBettinaW