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Here's my setup:

Independent Variables (IV):
(A) Task -- values 0 - 6 (order doesn't matter)
(B) Viewpoint -- values 0 - 26 (order doesn't matter)
(C) Input-device -- values {touchscreen, mouse, trackpad}

Dependent Variable (DV):
(1) Types of drawing -- values {arrow, circle, outline, arrow+circle, arrow+outline, circle+outline, arrow+circle+outline, sketch, words, ...}

I want to see if task, viewpoint, or input-device affects the type of drawing my participants did. What statistical test should I use for this?

Since this is all categorical (nominal) data, I was thinking to use the Chi-Squared test, but I have too many independent variables, right? All the websites I have found mention using Chi-Squared with only 1 independent variable. I can't use a "Factorial logistic regression" either because the dependent variable is not dichotomous. Any ideas?

EDIT: Actually, I think my dependent variable is the number of each of type of drawing drawn. E.g., for Task 0, Viewpoint 1, mouse, across all users who did this task (it's between-subjects on Task), there was 3 arrows, 5 circles, etc. This is still a categorical DV, right?

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  • $\begingroup$ I think that you need to clarify whether you really want to find out, if your IVs affect your DV, as, strictly speaking, this would be a causal analysis. Alternatively, your (most likely and simpler) goal is determine the nature of the relation between your IVs and your DV, which is a correlational analysis. But this is just my opinion. $\endgroup$ – Aleksandr Blekh Apr 9 '15 at 8:06
  • $\begingroup$ Yes, I think I want the latter--just the nature of the relation between my IVs and my DV. $\endgroup$ – t2k32316 Apr 9 '15 at 8:09
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I would suggest you the following high-level data analysis strategy/workflow:

  1. Start with performing exploratory data analysis (EDA). This will provide you with a sense of your data set as well as reveal the data set's features, which might be helpful in further steps (assumptions, etc.).

  2. Perform regression analysis. Your statement about inability of using logistic regression is incorrect, but this due to confusion that the term logistic regression often is used to refer to a model with a binary DV. Indeed, logistic regression is applicable in your case and is referred to as multinomial logistic regression, since your DV is of unordered categorical type. Should your DV be ordered, then that would be a case of an ordered logistic regression. The analysis IMHO should include evaluating the model's goodness-of-fit (GoF) and other relevant metrics (see above-referenced articles as a starting point, including for information on tests, etc.).

  3. Interpret the results of your analysis, based on your research goals and questions.

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