Problem Step 1: I have 10 variables on women decision making (Banking, Argument, Sexual Intercourse, Child rearing, Cooking, Land owning, Expenses, Outdoor visit, Buying products, & Health care). All of them have binary responses Yes/No.
Problem Step 2: I need to make a single variable composed of these 10 variables that can truly represent the 'Decision-making power/Women Autonomy' in the domestic sphere.
Problem Step3: I want to get comprehensive suggestions on statistical analysis/Modelling/Alternative ways of dealing with this matter.
Thanks in advance.
You can undertake a factor analysis of binary outcomes. this approach is sometimes known as item response theory (IRT but it is not a theory!). A key question is whether there is a single underlying 'response' ( a Rasch model) or more than one. The Mplus software has a very good and flexible implementation https://www.statmodel.com/irtanalysis.shtml
This is an excellent account with examples D. J. Bartholomew, Fiona Steele, Jane Galbraith, Irini Moustaki (2008) Analysis of Multivariate Social Science Data (Second edition), Chapter 8 Factor analysis for binary data
http://www.bristol.ac.uk/cmm/team/fs/aimdss-2nd-ed/chapter8.pdf
The data and syntax used in this chapter are at
http://www.lse.ac.uk/statistics/research/Social-Statistics/Multivariate-Data-Analysis/Data-and-Syntax
The syntax is for the following software
GENLAT LAMI (You will need to download this to run GENLAT) Mplus R SPSS STATA
Chapter 9 covers ordered categorical variables.
Dear Akash Mallick
I kindly suggest you to use multiple correspondence analysis. Greenacre is a reference author on this subject.
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