I’m revising a manuscript to resubmit to a journal that requires “that all statistical tests be reported fully to include the test statistic, its value, and its significance.” This manuscript includes results from a discrete choice experiment that we analyzed using latent class analysis. Typically I report the mean zero-centered/rescaled effects coded utilities for each class, their 95% confidence intervals, and a comparison across classes to tell whether the utilities for each level are different across class using a Wilcoxon rank sum test. I think, now, that this might be incorrect for latent class analysis, and instead I should report the t-statistics for each utility estimate that indicate, within each class and attribute, whether each utility estimate is different from zero. However, when I export the raw utilities and class membership into R and compute the means and standard deviations or variances, I can’t recover the standard error or t-ratios that Sawtooth includes in the Export Report summary from the standard deviation or variance. I am using the gtsummary package in R to summarize the individual-level utilities from Lighthouse Studio (that is, I am not using a package in R to re-estimate the utilities, I am just summarizing the outout from Lighthouse Studio).
My questions:
The estimates in the Export Report summary file for a given solution are from the “best replication.” Are the individual-level values exported from the Data Management window also from the best replication?
If the individual-level values are from the best replication, should I be able to get the same summary values for each utility and standard error by summarizing in a different application? If not, why not?
How do I calculate the standard errors and t-ratios from either the individual-level raw utility or rescaled utility values exported from the Data Management window? I have seen other posts that mention the standard definition of standard error (standard deviation/square root of sample size) and an alternative calculation (square root of variance). Is there other output I need to be using? If so, how do I get it?
Are the t-ratios calculated using the raw utility estimates equivalent to t-ratios that would be calculated using rescaled utility estimates? Because the rescaled utilities may be dispersed differently around zero than raw utilities, I didn't want to assume that the statistical tests would be the same for both sets of utilities.
As a point of clarification, in Chapter 12 of "Becoming an Expert in Conjoint Analysis," the text refers to coefficients and part-worth utilities, but the Exhibits use the word "Effect." Are these terms all synonymous? In the output from Sawtooth, when is something called or interpreted as a "coefficient," an "effect," and/or as a "part-worth utility"?
FWIW, I’m running Lighthouse Studio 9.16.16. Thanks in advance for your help!