Chi square for three categorical variables

Can I use chi square test with three variables ? The variables are organizational climate (11 dimensions), job satisfaction (7 dimensions) and customer satisfaction (5 dimensions). Likert scale. any suggestions.

• Your variables are ordered, you'll potentially be losing a lot of information about ordered dependence (including but not limited to monotonic correlation) if you treat them all as nominal (whether you do so depends on how general the alternatives you most care about are) May 15 at 1:07

However, it's probably not going to work very well or provide any meaningful statistics. I presume when you say each variable has $$k$$ "dimensions," you mean factor (or Likert*) levels. If so, then your 3-way table would have $$11 \times 7 \times 5 =385$$ frequency cells, requiring at least 2000 observations to get any reasonable expected values for the chi-square test (which likes the expected values to all be 5 or more).