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I am running multigroup singlefactor 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? 


My first thought would be to use the NEW option of the MODEL CONSTRAINT command to create the ratio parameter. 


Linda  This worked great. Thanks. Is there a short was to get sorted out about standard vs residual bootstrap ad the biascorrected bootstrap? Thanks 


Standard and residual are types of bootstrapping. Biascorrected bootstrap is a type of confidence interval. 


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 biascorrection do? As a rule, wouldn't someone always want bias corrected bootstrap? Thanks 


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, 99128. 


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? 


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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