Goodness-of-fit tests for a logistic regression model with missing covariates

Area of Science:

• Statistics
• Biostatistics
• Econometrics

Background:

• Logistic regression is widely used, but handling missing covariates is challenging.
• Existing methods for missing data in logistic regression may lead to biased results or underestimated variances.
• Goodness-of-fit testing is crucial for model validation in statistical modeling.

Purpose of the Study:

• To develop and evaluate novel goodness-of-fit tests for logistic regression models with missing covariates at random.
• To address the issue of variance underestimation encountered with standard multiple imputation methods.
• To provide robust statistical tools for assessing the validity of logistic regression models in the presence of missing data.

Main Methods:

• Proposed two types of goodness-of-fit tests: Pearson chi-squared and unweighted residual sum-of-squares.
• Employed inverse probability weighting (IPW) and nonparametric multiple imputation (MI) to handle missing covariate data.
• Developed IPW and bootstrap resampling approaches for accurate variance estimation of test statistics.
• Established asymptotic properties of the proposed test statistics under regularity conditions.

Main Results:

• The proposed test statistics, when centralized, exhibit mean-zero properties.
• Test statistics derived from IPW and MI estimators are asymptotically equivalent.
• IPW and bootstrap methods provide more reliable variance estimation compared to standard MI.
• Simulation studies demonstrate the finite-sample power of the proposed tests.

Conclusions:

• The developed goodness-of-fit tests are effective for logistic regression with missing covariates.
• The proposed variance estimation techniques overcome limitations of existing methods.
• The methods are applicable to real-world data, enhancing model checking capabilities.