A Martingale Residual Diagnostic for Logistic Regression Model

Martingale model diagnostic for assessing the fit of logistic regression model to recurrent events data are studied. One way of assessing the fit is by plotting the empirical standard deviation of the standardized martingale residual processes. Here we used another diagnostic plot based on martingale residual covariance. We investigated the plot performance under several types of model misspecification. Clearly the method has correctly picked up the wrong model. Also we present a test statistic that supplement the inspection of the two diagnostic. The test statistic power agrees with what we have seen in the plots of the estimated martingale covariance.

• Entisar A. Elgmati

• Covariance
• logistic model
• misspecification
• recurrent events.

[1] O. Aalen, A model for non-parametric regression analysis of counting
processes. Lecture Notes in Statistics, no. 2, pp. 1-25, 1980.
[2] E. Elgmati, D. Farewell, and R. Henderson, "A martingale residual
diagnostic for longitudinal binary or recurrent event data," Lifetime
Data Analysis, vol. 16, pp. 118-135, 2010.
[3] P. Diggle, D. Farewell, and R. Henderson, "Analysis of longitudinal
data with drop-out: objective, assumptions and a proposal (with
discussion)," Journal of the royal statistical society: Series C
(Applied Statistics), vol. 56, pp.499-550, 2007.
[4] E. Elgmati, " Logistic regression model versus additive model for
recurrent event data," in Proc. 3rd ICMLC, Singapore, Feb. 2011.
[5] J. Fosen, O. Borgan, H. Weedon-Fekjaer, and O. Aalen, "Dynamic
analysis of recurrent event data using the additive hazard model,"
Biometrical Journal, vol. 48, pp. 381-398, 2006.
[6] O. Aalen, J. Fosen, H. Wedon-Fekjaer, O. Borgan, and E. Husebye,
"Dynamic analysis of multivariate failure time data," Biometrics, vol.
60, pp. 764-773, 2004.
[7] O. Borgan, R. L. Fiaccone, R. Henderson, M. L. Barreto, "Dynamic
analysis of recurrent event data with missing observations, with
application to infant diarrhoea in Brazil ," Scandinavian Journal of
Statistics , vol. 34, pp. 53-69, 2007.
[8] E. Elgmati, R. L. Fiaccone, R. Henderson, and M. Mohammadi,
"Frailty modeling for clustered recurrent incidence of diarrhea,"
Statistics in Medicine, vol. 27, pp. 6489-6504, 2008.
[9] M. Barreto, L. Santos, A. Assis, M. Araujo, G. Farenzena, P. Santos,
and R. Fiaccone, " Effect of vitamin A supplementation on diarrhoea
and acute lower -respiratorytract infections in young children in
Brazil," Lancet, vol.344, pp. 228-231, 1994.