# Analysis of ordered-categorical data

Amos performs Bayesian model fitting for ordered-categorical data. As an example of ordered-categorical data, consider the response scale

A. Disagree

B. No opinion

C. Agree

One non-optimal method of handling responses on this scale is to assign numerical scores to the three response alternatives, for example A=1, B=2, C=3. With Bayesian estimation, Amos can employ a model in which there is a continuous underlying “agreement” scale that is broken up into three contiguous intervals. The observed categorical response is related to the unobserved numeric variable by the following rule. If a respondent’s level of agreement is in the lowest interval, the response is “A”. In the middle interval the response is “B”. In the highest interval the response is “C”. The distribution (across respondents) of the underlying numeric agreement score is assumed to be normal.

The following videos show how to fit a factor analysis model using ordered-categorical data.

- Recoding the data (12:06)
- Fitting a factor analysis model (7:43)
- Predictive distributions (estimating unknown data values) (7:18)
- Predictive distributions for factor scores (6:07)
- Imputation (8:24)

The above videos are based on Example 33 in the user's guide (English/Japanese).