On the Linearity Test based on CERES

Conditional Expectations and RESiduals(CERES) plots may be useful for obtaining an impression of curvature as a function of selected covariates x2 in regression problems in which the covariate vector x is partitioned as x^{ T } ``=``(x_{ 1 } ^{ T } ,x_{ 2 } ^{ T } ) In this paper, we consider the problem of checking the linearity of selected covariates x2 hrough the idea of smoothing of a CERES plot. A modified pseudo-likelihood ratio test statistic is derived as a ratio of quadratic forms. The distribution of this statistic is calculated numerically by using Johnson curves. Monte Carlo simulation is conducted to show the power of the test for small sample sizes.