Ridge traces

Probability plot Q-Q plot P-P Plot Hanging histogram Rootagram Poissonness plot Average versus standard deviation Component-plus-residual plot Partial-residual plot Residual plots Control chart Cusum chart Half-normal plot Ridge trace Youden plot... 

Standardized ridge estimates (3j with j = 1, , m are calculated for a range of values of k and plotted versus k. This plot is called a ridge trace. The /3 estimates usually change dramatically when k is initially incremented by a small amount from 0. As k is increased, the trace stabilizes. A k value that stabilizes all /3 coefficients is selected and the final values of j3 are estimated. 

Setting the c value is a trial-and-error process. Although c is generally a value between 0 and 1, many statisticians urge the researcher to assess 20 to 25 values of c. As c increases from 0 to 1, its effect on the regression parameters can vary dramatically. The selection procedure for a c value requires a ridge trace to find a c value where the fe values are stabilized. 

Note that each of the Ci values is chosen arbitrarily by the researcher. The next step (Step 4) is to plot the ridge trace data (Table 6.11). The values are rounded to three places to the right of the decimal point. 

The next step (Step 5), using the complete ridge trace plot, is to pick the smallest value c, in which the betas, b, are stable— that is, no longer oscillating wildly or with high rates of change. In practice, the job will be... 

FIGURE 6.9 Complete ridge trace plot Scatterplot of c vs. b values. 

The choice of k belongs to the analyst and should be chosen where strong evidence shows more stable estimates or improved prediction. One method suggested by Hoerl and Kennard (1970) is the use of a ridge trace. The ridge trace is a plot of the b. vs. k, usually in the interval (0, 1). For values close to A = 0, intercorrelation will cause rapid changes in b. The objective is to select a small value of k where the /s stabilize. 

Figure 7 Ridge trace for the eleven regression coefficients for the data set generated for use in the multicolinearity detection example.

Because of the subjectivity attached to the ridge trace approach for finding the best value for d, many automatic alternative methods have been offered in the literature. The two that appear more frequently are given in Eqs. [18] and [19]. 

Wood, D.A., Jordon, J.L., Marsh, N.G., Tamey, J. and Greuil, M. (1980) Major and trace element variations drilled in basalts from the North Philippine Sea during Deep Sea Drilling Project Leg 58 A comparative study of back-arc basin basalts with lava series from Japan and midocean ridges. Deep Sea Drilling Project, Initial Reports, 58, 827—894. 

Salters VJM, Longhi J (1999) Trace element partitioning during the initial stages of melting beneath midocean ridges. Earth Planet Sci Lett 166 15-30... 

Reiter, E. R. Transport in the planetary boundaiy layer, pp. 127-182. In Atmospheric Transport Processes. Part 3 Hydrodynamic Traces. AEC Critical Review ries. TID-25731. Oak Ridge, Tenn. U.S. Atomic Energy Commission, 1972. 

Fig. 12. Asymmetry of the DNA phosphodiester backbone trace as seen in the Oak Ridge NCP structural model (PDB access code lEQZ). No attempt has been made to regularize the geometry of the DNA positions of phosphates are based solely on the experimental electron density. Here the two DNA gyres are overlaid, with the 72 bp ventral gyre in red and the 73 bp dorsal gyre in blue. The minor groove positions facing the histone core are numbered sequentially from the dyad axis. The most pronounced asymmetry is seen in position 2 (10 o clock).

Fig. 13. Salient features of the GC-MS data for the saturated fraction of a hydrothermal bitumen sam pie from the Mid-Atlantic Ridge (a) TIC - background trace, (b) ra/z 85 fragmentogram (key ion for 3-ethyl-3-methylalkanes and -alkanes), (c) mjz 99, key ion for 3,3-diethylalkanes with -alkanes, and (d) m/z 127, key ion for 5,5-diethylalkanes with w-alkanes. (Numbers refer to total carbon number, dots ovet peaks are -alkanes.)... 

A second example is shown in excerpt 13Q. Harpp s proposed work initially involves the collection of held data in two sampling campaigns. Following collection, the samples will be analyzed for trace and major element concentrations and isotopic ratios. In her case, the order in which she conducts these analyses is less important than how she will use the data to answer questions about plume-ridge interaction mechanisms. Thus, she organizes her proposed work (titled Proposed Plan ) not by the tests she will perform, but rather by the types of information the analyzed data will provide (i.e., information about formation mechanisms, melting dynamics, and spatial distributions). 

Year Five Complete analysis of trace elements by ICP-MS at Lawrence University analysis of major elements by XRF at Macalester College (up to 100 samples) determination of Sr, Nd, and Pb isotopic ratios of a selection of Wolf and Darwin samples by TIMS at Cornell (up to 30 samples). Interpretation of geochemical data, modeling of melting parameters. Presentation of results at Fall AGU meeting by undergraduate student(s). Preparation of final plume-ridge interaction synthesis paper for publication with student authors. 

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