rqlm: Modified Poisson and least-squares regression analyses for...

In rqlm: Modified Poisson, Logistic and Least-Squares Regressions for Binary Outcome and Their Generalizations

Modified Poisson and least-squares regression analyses for binary outcomes

Description

Modified Poisson and least-squares regression analyses for binary outcomes are performed. This function is handled by a similar way with lm or glm. The model fitting to the binary data can be specified by family. Also, the resultant coefficients and confidence limits can be transformed to exponential scales by specifying eform. The Morel-Bokossa-Neerchaal-type small-sample corrected estimator is adopted for standard error estimation as the default method.

Usage

rqlm(formula, data, family=poisson, eform=FALSE, cl=0.95, digits=4, var.method="MBN")

Arguments

formula	An object of class "formula" (or one that can be coerced to that class): a symbolic description of the model to be fitted.
data	A data frame, list or environment (or object coercible by as.data.frame to a data frame) containing the variables in the model.
family	A description of the error distribution and link function to be used in the model. gaussian: Modified least-squares regression. poisson: Modified Poisson regression.
eform	A logical value that specify whether the outcome should be transformed by exponential function (default: FALSE)
cl	Confidence level for calculating confidence intervals (default: 0.95)
digits	Number of decimal places in the output (default: 4).
var.method	Method for estimating standard errors. Standard robust variance estimator (standard) and Morel-Bokossa-Neerchaal-type corrected estimator (MBN) are available (default: MBN).

Value

Results of the modified Poisson and least-squares regression analyses.

• coef: Coefficient estimates; transformed to the exponential scale if eform=TRUE.

• SE: Robust standard error estimates for coef.

• CL: Lower limits of confidence intervals.

• CU: Upper limits of confidence intervals.

• P-value: P-values for the coefficient tests.

References

Cheung, Y. B. (2007). A modified least-squares regression approach to the estimation of risk difference. American Journal of Epidemiology 166, 1337-1344.

Gosho, M., Ishii, R., Noma, H., and Maruo, K. (2023). A comparison of bias-adjusted generalized estimating equations for sparse binary data in small-sample longitudinal studies. Statistics in Medicine 42, 2711-2727.

Morel, J. G., Bokossa, M., and Neerchal, N. (2003). Small sample correction for the variance of GEE estimators. Biometrical Journal 45, 395-409.

Noma, H. and Gosho, M. (2025). Finite-sample improved confidence intervals based on the estimating equation theory for the modified Poisson and least-squares regressions. Epidemiologic Methods 14, 20240030.

Noma, H., Sunada, H., and Gosho, M. (2025). Quasi-likelihood ratio tests and the Bartlett-type correction for improved inferences of the modified Poisson and least-squares regressions for binary outcomes. Statistica Neerlandica 79, e70012.

White, H. (1982). Maximum likelihood estimation of misspecified models. Econometrica, 50, 1-25.

Zou, G. (2004). A modified poisson regression approach to prospective studies with binary data. American Journal of Epidemiology 159, 702-706.

Examples

data(exdata02)

rqlm(y ~ x1 + x2 + x3 + x4, data=exdata02, family=poisson, eform=TRUE)
# Modifed Poisson regression analysis
# Coefficient estimates are translated to risk ratio scales

rqlm(y ~ x1 + x2 + x3 + x4, data=exdata02, family=gaussian)
# Modifed least-squares regression analysis

rqlm(y ~ x1 + x2 + x3 + x4, data=exdata02, family=gaussian, digits=3)
# Modifed least-squares regression analysis
# Number of decimal places can be changed by specifying "digits"

rqlm documentation built on Nov. 23, 2025, 5:06 p.m.