Biology Reference
In-Depth Information
FIGURE 11-21.
COSIN2NL analysis of the noisy nonstationary cosine wave originally presented in Figure 11-15. As in
Figure 11-20, COSIN2NL performed a single-component cosine analysis in which five parameters
were nonlinear least squares (NLLS) estimated (Amp, Per, Phi, DC, and Slop; where DC refers to
the estimated value at time zero on the x-axis). NLLS was performed by a modified Gauss-Newton
method. The convergence criterion was set to a fractional change in variance of 10
9
. Approximate
nonlinear asymmetric joint confidence limits were calculated at 95% confidence (in which lower and
upper parameter confidence limits are estimated independently; the values reported in parentheses;
the values reported following รพ/ are one-half the difference between the estimated upper and
lower confidence limits). The results of this analysis thus indicate that (1) the estimated oscillatory
amplitude is 38.4 9.2 y-axis units; (2) the estimated period is 23.31 0.20 hours; (3) the estimated
phase is 2.5 1.0 hours; (4) the estimated value at time zero (DC) is 733.5 7.4 y-axis units; and
(5) the estimated slope is 3.478 0.053 y-axis units per hour.
set from Figure 11-14). Notice, however, that the model does not
accommodate the data from Figure 11-15 particularly well (see
Figure 11-21). Indeed, assuming a linear trend is not realistic for the data
set in Figure 11-15. Also, as the model assumes a single cosine wave; it is
not capable of capturing the decreasing oscillatory amplitudes that
are apparent in Figure 11-15. As a result, COSIN2NL is incapable
