# Calculating standard errors of effects coded part-worths in CBC/Logit

Hello Sawtooth,

for a thesis in the course "market research" at my university I should reproduce the results of the CBC/Logit analysis of a given conjoint study made with SSi-Web. For a deeper understanding of conjoint, my teachers said I should use the statistical software R.

Now my problem: With the effect coding of the data set, I conducted a maximum likelihood estimation with a existing R-function. I have nearly the same results as SSi but, now the problem, just 17 values from 23 attribute levels with 6 attributes (sum(levels) - #attributes). I know how to calculate the missing effects through the effects coding, but I do not understand how I can calculate the standard error of the missing part-worths in the estimation. Can you help me with this, please? Is there a way to calculate the missing standard errors from the estimated ones?

The standard errors are calculated as follows:

For part-worth coding, the first n-1 levels are simply the square root of the diagonal value from the estimated variance/covariance matrix.  The omitted level is the square root of the sum of the variances & covariances for that attribute.  For example, assuming a very simple variance/covariance matrix:

a b c 0 0 0
d e f 0 0 0
g h i 0 0 0
0 0 0 j k l
0 0 0 m n o
0 0 0 p q r

For attribute 1 (a 4 level attribute), the omitted level 4's standard error is the square root of the sum of elements a-i.

For linear (continuous) terms, the standard error is similarly the square root of the diagonal value from the matrix.
answered Jun 10, 2014 by Gold (19,280 points)