Figure 2.

Results of three separate simulation runs. The center histogram shows the estimated value $\widehat{\psi }(y=1)$ when a linear logistic regression model is fit to data generated from model (Eq. 8). The histogram summarizes B = 1000 different runs, each consisting of 1000 presence samples. The true value of Ψ(y = 1) is given by the vertical red line. The two flanking histograms change the 1/2 in (Eq. 8) to C = 3/10 (left) and C = 7/10 (right), with again the red line showing the true value of Ψ(y = 1). In all cases, irrespective of the true value of Ψ(y = 1), the histograms indicate that the value being estimated is centered around Ψ(y = 1) ≈ 0.33, the value from Eq. (3).