Table 1.

% Bias (MSE in parentheses) for population slope for population generated under $Y_i\mid X_i\sim N(A+{BX}_i+C{X}_i^2,1)$, i = 1,…, 10000, and superpopulation model is given by Y_i |X_i ~ N (α + βX_i, σ²): correctly specified (A = 0, B = 2, C = 0), misspecified (A = 0, B = 2, C = −1). Sampling design ignorable population slope (P(S_i|Y_i,X_i)∝X_i̇⁷⁵) or non-ignorable for population slope (P (S_i |Y_i, X_i) ∝ exp(.5Y_i/(X_i + .25) − 1)). Results from 500 simulations.

	Sampling ignorable?
	Yes		No
	Superpopulation model correctly specified?
	Yes	No	Yes	No
n=50
β̂	−0.2(.168)	−15.4(.203)	−30.8(.511)	−63.8(.518)
β̂w	0.7(.264)	−3.8(.274)	−5.1(.239)	−10.5(.303)
n=500
β̂	−0.5(.015)	−16.3(.040)	−28.6(.339)	−55.7(.321)
β̂w	−0.8(.033)	−0.3(.032)	−.7(.039)	0.0(.041)