Figure 6.
Assessments of the goodness- and randomness-of-fit. **
***a–c*
, Mean and confidence intervals (±2 SEM) of the vertical differences (residual probability) between the observed probability and that predicted by the best fits of models Ia (**
***a*
), Ib (**
***b*
), and II (**
***c*
) plotted as a function of the observed probability. Observed probabilities were obtained at 10,000 points, equally spaced along the abscissa, by linear interpolation, and mean residuals at these points were obtained by averaging the residuals across the 186 samples of stable spontaneous activity. In this way, unsystematic residuals primarily average out, whereas systematic differences remain. Note the large systematic residuals of model Ia and the much smaller residuals of model II. The goodness-of-fit, as assessed by the sum of the squared vertical (sqd. vert.) differences, is ∼30 times better for model II than for Ia, and 2.5 times better than for Ib. Arrowheads point to conspicuous features of the mean function or of the confidence limits, as explained in the Results. **
***d–f*
, Analogous plots obtained from fits of models Ia (**
***d*
), Ib (**
***e*
), and II (**
***f*
) to 186 simulated data samples generated according to model II and with fixed values of *t*
_{D}, 1/λ_{R}, and *b*, *t*
_{D} = 0.59 ms, 1/λ_{R} = 0.65 ms, and *b* = 0.43 and with numbers of ISIs as in the real data. Note the striking similarities with the estimates obtained from the real data. The light gray smooth M-shaped function in **
***f*
represents the mean residuals obtained from fits to 162 such simulated sets of 186 samples each. It likely reflects the residuals inherent in the fitting procedure when confronted with random data. **
***g–i*
, Differences between the mean vertical differences in the real data (**
***a–c*
, black lines) and the procedure-inherent residuals (light gray function in **
***f*
) and associated confidence interval. For model II (**
***i*
), these corrected residuals are very small and confined within the 95% confidence interval, except at very low probabilities (inset). See Results for details.