In Martyna et al

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In Martyna et al. (2013) (The evidential value of microspectrophotometry measurements made for pen inks. Analytical Methods) the authors are focused on developing a type of similarity score, between two ink samples, known as a forensic likelihood ratio. We are interested in three of the univariate LR's (corresponding to the "X", "Y", and "Z" measures of color) that were constructed and their relationship to an omnibus LR that I (Dr. Saunders) constructed. Please describe and characterize the relationship between the 4 forensic likelihood ratios, with the ultimate aim of predicting the omnibus Likelihood ratio in terms of the three univariate likelihood ratios. Note that all of the likelihood ratios are given on a "log" scale. There is one csv file that contains the data for this study. The file is "dat.LLR.int.csv" it has six columns containing: Comp o Comparison of interest (from 1 to 820). Omni.LLR.int o numeric values of for the Log of the Omnibus likelihood ratio, this is the response variable we are interested in. Type o Type of comparison, either "wi" for within-source comparison or "bw" for between-source comparison LLR.x o The Log Likelihood ratio for the X color variable LLR.y o The Log Likelihood ratio for