## Brazilian Journal of Probability and Statistics

- Braz. J. Probab. Stat.
- Volume 28, Number 1 (2014), 109-139.

### A product-multinomial framework for categorical data analysis with missing responses

Frederico Z. Poleto, Julio M. Singer, and Carlos Daniel Paulino

#### Abstract

With the objective of analysing categorical data with missing responses, we extend the multinomial modelling scenario described by Paulino (*Braz. J. Probab. Stat.* **5** (1991) 1–42) to a product-multinomial framework that allows the inclusion of explanatory variables. We consider maximum likelihood (ML) and weighted least squares (WLS) as well as a hybrid ML/WLS approach to fit linear, log-linear and more general functional linear models under ignorable and nonignorable missing data mechanisms. We express the results in an unified matrix notation that may be easily used for their computational implementation and develop such a set of subroutines in R. We illustrate the procedures with the analysis of two data sets, and perform simulations to assess the properties of the estimators.

#### Article information

**Source**

Braz. J. Probab. Stat., Volume 28, Number 1 (2014), 109-139.

**Dates**

First available in Project Euclid: 5 February 2014

**Permanent link to this document**

https://projecteuclid.org/euclid.bjps/1391611341

**Digital Object Identifier**

doi:10.1214/12-BJPS198

**Mathematical Reviews number (MathSciNet)**

MR3165432

**Zentralblatt MATH identifier**

06291464

**Keywords**

EM algorithm incomplete data missing data missingness mechanism selection models

#### Citation

Poleto, Frederico Z.; Singer, Julio M.; Paulino, Carlos Daniel. A product-multinomial framework for categorical data analysis with missing responses. Braz. J. Probab. Stat. 28 (2014), no. 1, 109--139. doi:10.1214/12-BJPS198. https://projecteuclid.org/euclid.bjps/1391611341