Interpreting MICOM output

[humcasma]

I am using the MICOM procedure to test for measurement invariance among groups in my model. The output of SmartPLS in MICOM's Step 3 for one of my LVs is as follows:

Orig. mean: -0.264
Perm. mean: 0.001
CI 5%: [-0.056, 0.056]
p-value: 0

So, according to the p-value, the difference of means is statistically significant, so there is no full measurement invariance.
However, in page 416 of the original MICOM paper [1], the authors say:
"If the confidence intervals of differences in mean values (and logarithms of variances) between the construct scores of the first and second group
include zero, the researcher can assume that the composite mean values (and variances) are equal. In this case, full measurement invariance has been established"

In my case, the CI includes zero, so according to the paper we could claim that the composite mean values are equal. This is in contradiction to what the p-value says. So how should I interpret this result?

On a side note, how is the CI calculated here? When reading literature about permutation tests, I always read about calculating p-values, but no CIs.

Cheers,
Nicolás

[1] Henseler, J., Ringle, C.M. and Sarstedt, M. (forthcoming), “Testing measurement invariance of
composites using partial least squares”, International Marketing Review.

[ferry.jaolis]

I have the same problem of interpreting the output of MICOM Step 3. The MICOM paper makes a confusing statement about looking at the CI and the result of p-values from MICOM report in smartpls 3. Reading the CI and if there is zero in the lower and upper bound meaning equal means and variances are achieved and hence full measurement invariance is established (i.e according to MICOM paper). Yet in my data I have found there were zeros in the CI upper and lower bound (i.e. full measurement invariance) but the p-values were respectively sig. lower than 5% (i.e. full measurement invariance is not established). Which one to refer, CI or p-values? Please if anyone could clarify this. Huge thanks in advance.


Best,
Ferry

[Lilia]

Hallo Ferry and Nicolas,
I have the same problem. Have you found a clarification?
I am looking forward to hearing from you soon and Big Thanks in advance,
Best wishes,
Lilia

[jmbecker]

The sentence in the paper is wrong.
It should be: “If the permutation confidence intervals of differences in mean values and logarithms of variances between the construct scores of the first and second group include the original difference, the researcher can assume that the composite mean values and variances are equal.”

The confidence intervals are calculted based on all the permutations using the percentile method. While Permutation-P values count the number of values larger (or smaller) than the original difference, this approach is very similar and should give the same conclusions. If the original value would be equal to one of the 95% confidence interval limits, it would give a Permutation P-value of 5%.