### Abstract

When estimating multiple regression models with incomplete predictor variables, it is necessary to specify a joint distribution for the predictor variables. A convenient assumption is that this distribution is a multivariate normal distribution, which is also the default in many statistical software packages. This distribution will in general be misspecified if predictors with missing data have nonlinear effects (e.g., x^{2}) or are included in interaction terms (e.g., x·z). In the present article, we introduce a factored regression modeling approach for estimating regression models with missing data that is based on maximum likelihood estimation. In this approach, the model likelihood is factorized into a part that is due to the model of interest and a part that is due to the model for the incomplete predictors. In three simulation studies, we showed that the factored regression modeling approach produced valid estimates of interaction and nonlinear effects in regression models with missing values on categorical or continuous predictor variables under a broad range of conditions. We developed the R package mdmb, which facilitates a user-friendly application of the factored regression modeling approach, and present a real-data example that illustrates the flexibility of the software.

Original language | English (US) |
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Journal | Multivariate Behavioral Research |

DOIs | |

State | Accepted/In press - Jan 1 2019 |

### Fingerprint

### Keywords

- interaction effects
- maximum likelihood estimation
- missing data
- Multiple regression

### ASJC Scopus subject areas

- Statistics and Probability
- Experimental and Cognitive Psychology
- Arts and Humanities (miscellaneous)

### Cite this

**Analysis of Interactions and Nonlinear Effects with Missing Data : A Factored Regression Modeling Approach Using Maximum Likelihood Estimation.** / Lüdtke, Oliver; Robitzsch, Alexander; West, Stephen.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - Analysis of Interactions and Nonlinear Effects with Missing Data

T2 - A Factored Regression Modeling Approach Using Maximum Likelihood Estimation

AU - Lüdtke, Oliver

AU - Robitzsch, Alexander

AU - West, Stephen

PY - 2019/1/1

Y1 - 2019/1/1

N2 - When estimating multiple regression models with incomplete predictor variables, it is necessary to specify a joint distribution for the predictor variables. A convenient assumption is that this distribution is a multivariate normal distribution, which is also the default in many statistical software packages. This distribution will in general be misspecified if predictors with missing data have nonlinear effects (e.g., x2) or are included in interaction terms (e.g., x·z). In the present article, we introduce a factored regression modeling approach for estimating regression models with missing data that is based on maximum likelihood estimation. In this approach, the model likelihood is factorized into a part that is due to the model of interest and a part that is due to the model for the incomplete predictors. In three simulation studies, we showed that the factored regression modeling approach produced valid estimates of interaction and nonlinear effects in regression models with missing values on categorical or continuous predictor variables under a broad range of conditions. We developed the R package mdmb, which facilitates a user-friendly application of the factored regression modeling approach, and present a real-data example that illustrates the flexibility of the software.

AB - When estimating multiple regression models with incomplete predictor variables, it is necessary to specify a joint distribution for the predictor variables. A convenient assumption is that this distribution is a multivariate normal distribution, which is also the default in many statistical software packages. This distribution will in general be misspecified if predictors with missing data have nonlinear effects (e.g., x2) or are included in interaction terms (e.g., x·z). In the present article, we introduce a factored regression modeling approach for estimating regression models with missing data that is based on maximum likelihood estimation. In this approach, the model likelihood is factorized into a part that is due to the model of interest and a part that is due to the model for the incomplete predictors. In three simulation studies, we showed that the factored regression modeling approach produced valid estimates of interaction and nonlinear effects in regression models with missing values on categorical or continuous predictor variables under a broad range of conditions. We developed the R package mdmb, which facilitates a user-friendly application of the factored regression modeling approach, and present a real-data example that illustrates the flexibility of the software.

KW - interaction effects

KW - maximum likelihood estimation

KW - missing data

KW - Multiple regression

UR - http://www.scopus.com/inward/record.url?scp=85070237530&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85070237530&partnerID=8YFLogxK

U2 - 10.1080/00273171.2019.1640104

DO - 10.1080/00273171.2019.1640104

M3 - Article

AN - SCOPUS:85070237530

JO - Multivariate Behavioral Research

JF - Multivariate Behavioral Research

SN - 0027-3171

ER -