 confounding between the model covariates and causal variables ( which may or may not be included as model covariates ) is a well - known problem in regression models used in air pollution epidemiology . 
 this problem is usually acknowledged but hardly ever investigated , especially in the context of generalized linear models . using synthetic data sets , 
 the present study shows how model overfit , underfit , and misfit in the presence of correlated causal variables in a poisson regression model affect the estimated coefficients of the covariates and their confidence levels . 
 the study also shows how this effect changes with the ranges of the covariates and the sample size . 
 there is qualitative agreement between these study results and the corresponding expressions in the large - sample limit for the ordinary linear models . 
 confounding of covariates in an overfitted model ( with covariates encompassing more than just the causal variables ) does not bias the estimated coefficients but reduces their significance . 
 the effect of model underfit ( with some causal variables excluded as covariates ) or misfit ( with covariates encompassing only noncausal variables ) , on the other hand , leads to not only erroneous estimated coefficients , but a misguided confidence , represented by large t - values , that the estimated coefficients are significant . 
 the results of this study indicate that models which use only one or two air quality variables , such as particulate matter [ less than and equal to ] 10 microm and sulfur dioxide , are probably unreliable , and that models containing several correlated and toxic or potentially toxic air quality variables should also be investigated in order to minimize the situation of model underfit or misfit.imagesfigure 1figure 2figure 3figure 4figure 5figure 6figure 7figure 8 
Images