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69in figure 4.1B). This problem causes the adjusted BIC to tend to underestimatethe number of segments because smaller models yield large R 2 values due to thelack of fit of the model.The BIC and adjusted BIC values for figure 4.1B are shown in table 4.1. Becausethe difference in loglikelihood is so large in this case, both the BIC and theadjusted BIC make the correct choice between one and two segments, though theunadjusted BIC is more decisive.An example of this problem with image data is given by figure 4.2 and table4.2. The image clearly has two segments, but the adjusted BIC (equation 4.80)incorrectly chooses one segment. An unadjusted BIC, i.e. equation 4.80 withoutthe R 2 term, correctly selects two segments in this relatively easy example. Themixture loglikelihood shows little change as more segments are added beyond two,which is consistent with the fact that only two segments are needed for this image.Table 4.2: Loglikelihood and BIC results for the image of figure 4.2.Number of Mixture Unadjusted AdjustedSegments Loglikelihood BIC BIC1 -2095 -4203 -32672 -1771 -3572 -36163 -1770 -3589 -36474 -1770 -3606 -3679