I am trying to analyze dichotomous/categorical data across several age groups and within each age group. The dichotomous/categorical data come from a decision task in which participant responses are classified into one of three decision types. The decision types are mutually exclusive (i.e., a participant's decision can only fall into one of the three categories). I want to analyze:
- Whether our 5 age groups differ in the proportion of each type of decision made (e.g., whether some age groups make Decision Type 1 more than other age groups)
- Whether the proportions of the three decision types differ within each age group (e.g., whether participants in Age Group 1 make Decision Type 1 more than Decision Type 2 and 3).
I have currently coded the decision type variable in two ways (see the attached for the data file setup):
- A single between-subjects variable with three levels corresponding to the decision type
- Three within-subjects variables (one for each decision type), where participants get assigned a "0" if they didn't make that decision type or a "1" if they did make that decision type.
Ideally, I want to look at the interaction between age group and decision type, and follow-up with simple effects and pairwise comparisons. The easiest way to do this seems to be a 5 (age group: between subjects) X 3 (decision type: within-subjects) ANOVA. However, the Decision Type variables are dichotomous, not normally distributed, and not really within-subjects. Is there another way to set up the data, or an alternative analysis/analyses that offer full resolution of this analysis from the omnibus test to the pairwise comparisons?
If I understand you you want a logistic regression on the LHS and a model of a longitudinal design on the RHS. The LHS is covered in Harrell's notes attached and the RHS by Davidian's notes at the link:
https://www.stat.ncsu.edu/people/davidian/courses/st790/notes.html
Best wishes, D. Booth
Thanks David Eugene Booth for the notes and suggestions, and Jos Feys for the R scripts!
Jos Feys, I plan to run your scripts on our full data set in the near future--would you be alright with me contacting you directly if I have additional questions about the analysis/interpretation? I'm new to R and would like to ensure I get everything right.
Hi Eric,
Yes, you can always contact me at: [email protected] or [email protected]
1)
I first ran the Fisher test to see if there is a relation between "age group" and 'decision type"
Frequency table:
Type group 1 2 3 1 2 1 0 2 1 1 1 3 1 0 2 4 0 0 3 5 0 1 2
The chi-square is not sign. (p-value = 0.4246), probably because too few observations.
2)
I then ran 5 Cochran tests for each age group to test the repeated 0/1 decision types. It turned out that only in the age group 4 or D, there is a sign effect of decision type.
agegroup4
As you count the number of participants, in case you have enough participants in each age group (more than five expected participants in each cell of the combionation age group x decision type), you can use Chi-Square to answer the first question.
Chi-Square is implemented in all statistical programm packages
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