CI for ratio of two factor loadings PreviousNext
Mplus Discussion > Confirmatory Factor Analysis >
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 Daniel E Bontempo posted on Friday, April 07, 2006 - 4:27 pm
I am running multi-group single-factor CFA with dichotomous indicators.

I would like to get a bootstrapped CI for the ratio of an items's loading in the 1st group and the corresponding item's loading in the 2nd group.

After using CI(bootstrap) to get CI's for the two loadings, is there a straightforward (or even not so straightforward) way to get a bootstrapped CI for the ratio?
 Linda K. Muthen posted on Friday, April 07, 2006 - 6:49 pm
My first thought would be to use the NEW option of the MODEL CONSTRAINT command to create the ratio parameter.
 Daniel E Bontempo posted on Tuesday, April 11, 2006 - 6:02 pm
Linda - This worked great. Thanks.

Is there a short was to get sorted out about standard vs residual bootstrap ad the bias-corrected bootstrap?

Thanks
 Linda K. Muthen posted on Tuesday, April 11, 2006 - 9:05 pm
Standard and residual are types of bootstrapping. Bias-corrected bootstrap is a type of confidence interval.
 Daniel E Bontempo posted on Friday, June 23, 2006 - 2:04 pm
Ok, I guess my real question was the difference between CINTERVAL(BOOTSTRAP) and CINTERVAL(BCBOOTSTRAP) - unlike SYMMETRIC, both seem to take the distributionof the bootstrap into account. Beyond taking the distribution into account what does bias-correction do? As a rule, wouldn't someone always want bias corrected bootstrap?

Thanks
 Linda K. Muthen posted on Friday, June 23, 2006 - 2:31 pm
I think you can find the answers in the following paper:

MacKinnon, D.P., Lockwood, C.M., & Williams, J. (2004). Confidence limits for the indirect effect: Distribution of the product and resampling methods. Multivariate Behavioral Research, 39, 99-128.
 Daniel E Bontempo posted on Friday, June 23, 2006 - 2:53 pm
More Specifically, the BCbootstrap does not seem to be working.

Here is the CINTERVAL(BOOTSTRAP) output for my ratios (as discussed above) and a few of the thresholds just above them.

CONFIDENCE INTERVALS OF MODEL RESULTS

Lower .5% Lower 2.5% Estimates Upper 2.5% Upper .5%
T1_82$1 0.255 0.329 0.489 0.652 0.700
T1_82$2 1.130 1.186 1.365 1.619 1.719
T1_89$1 0.715 0.790 1.006 1.299 1.426
T1_89$2 1.646 1.787 2.125 2.672 2.902

Variances
CD 0.000 0.000 1.000 0.000 0.000

New/Additional Parameters
CD05_OY 0.363 0.433 0.759 1.276 1.401
CD13_OY 0.488 0.630 1.075 2.142 2.883
CD28_OY 0.555 0.717 1.176 1.967 2.413
CD51_OY 0.560 0.676 1.140 1.974 2.162
CD54_OY 0.212 0.333 0.856 1.842 2.631
CD56_OY 0.362 0.450 0.788 1.265 1.438
CD58_OY 0.574 0.644 1.113 1.930 2.178
CD62_OY 0.618 0.677 1.130 1.764 2.045
CD63_OY 0.595 0.705 1.120 1.728 2.026
CD71_OY 0.647 0.781 1.350 2.429 2.954
CD78_OY 0.308 0.431 0.872 1.741 2.088
CD82_OY 0.137 0.218 0.486 0.899 1.140
CD89_OY 0.394 0.522 1.061 2.122 2.554


It all looks good. The 2.5% and 5% windows get wider around the point estimates and the intervals are not symmetrical.

However here is the CINTERVAL(BCbootstrap) output from the otherwise identical program:

CONFIDENCE INTERVALS OF MODEL RESULTS

Lower .5% Lower 2.5% Estimates Upper 2.5% Upper .5%
T1_82$1 0.255 0.317 0.489 0.645 0.673
T1_82$2 1.115 1.183 1.365 1.585 1.702
T1_89$1 0.715 0.790 1.006 1.288 1.424
T1_89$2 1.646 1.777 2.125 2.642 2.886

Variances
CD 0.000 0.000 1.000 0.000 0.000

New/Additional Parameters
CD05_OY 0.289 0.289 0.759 0.289 0.289
CD13_OY 0.454 0.454 1.075 0.454 0.454
CD28_OY 0.550 0.550 1.176 0.550 0.550
CD51_OY 0.527 0.527 1.140 0.527 0.527
CD54_OY -0.001 -0.001 0.856 -0.001 -0.001
CD56_OY 0.325 0.325 0.788 0.325 0.325
CD58_OY 0.548 0.548 1.113 0.548 0.548
CD62_OY 0.617 0.617 1.130 0.617 0.617
CD63_OY 0.592 0.592 1.120 0.592 0.592
CD71_OY 0.613 0.613 1.350 0.613 0.613
CD78_OY 0.278 0.278 0.872 0.278 0.278
CD82_OY 0.116 0.116 0.486 0.116 0.116
CD89_OY 0.286 0.286 1.061 0.286 0.286


The intervals for the thresholds are a little different, but close.

However, the output for the new parameters no longer appears to be interval endpoints, and the 2.5% and 5.0% now have the same value anyway.

Is this a big? Does BCbootstrap output not work right for new model parameters?
 Linda K. Muthen posted on Friday, June 23, 2006 - 3:11 pm
I believe this has been fixed. Are you using Version 4.1? If not, I suggest you download it. If you have the same problem in Version 4.1, you should send your input, output, and data to support@statmodel.com.
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