Modern Applied Statistics Assignment -

Q1: During the past week you have been working on a group assignment to analyze a specific data. As part of this exam please report on that project. This time the work has to be individual. You can still use the code generated as a group and modify/improve on it.

a. Provide a two-page write-up (including graphs) explaining your analysis of the dataset and the conclusions you can draw from it.

b. As a secondary component provide annotated code that replicates your analysis.

Q2: The file "y.csv" contains a dataset consisting of 200 observations and 6 variables. There are four groups in the dataset. For the first 160 observations you are given the true group memberships (ID's). In the dataset, the first variable represents the group membership of each observation. Your task is to build a certain model to classify the remaining 40 observations with "NA" Id's in the dataset.

a. Provide a page write-up (including graphs) explaining what methods you used for explanatory analysis and to model the groups and how you predicted the identity of the remaining 40 observations.

b. Provide an estimate of your error rate. Out of the 40 observations how many do you think you identified correctly?

c. As a secondary component provide annotated code that replicates your analysis.

Q3: (Vole Data)- Consider the microtus dataset in the Flury library in R.

Background from Airoldi et al. 1995:

Discrimination Between Two Species of Microtus using both Classified and Unclassified Observations.

Introduction : Microtus subterraneus and M. multiplex are now considered to be two distinct species (Niethammer, 1982; Krapp, 1982), contrary to the older view of Ellerman & Morrison-Scott (1951). The two species differ in the number of chromosomes: 2n=52 or 54 for M. subterraneus, and 2n=46 or 48 for M. multiplex. Hybrids from the laboratory have reduced fertility (Meylan, 1972), and hybrids from the field, whose karyotypes would be clearly recognizable, have never been found (Krapp, 1982). The geographic ranges of distribution of M. subterraneus and M. multiplex overlap to some extent in the Alps of southern Switzerland and northern Italy (Niethammer, 1982; Krapp, 1982). M. subterraneus is smaller than M. multiplex in most measurements, and occurs at elevations from 1000 m to over 2000 m, except in the western part of its range (for example, Belgium and Brittany), where it is found in lower elevations. M. multiplex is found at similar elevations, but also at altitudes from 200300 m south of the Alps (Ticino, Toscana). The two chromosomal types of M. subterraneus can be crossed in the laboratory (Meylan, 1970, 1972), but no hybrids have so far been found in the field. In M. multiplex, the two chromosomal types show a distinct distribution range, but they are morphologically indistinguishable, and a hybrid has been found in the field (Storch & Winking, 1977). No reliable criteria based on cranial morphology have been found to distinguish the two species. Saint Girons (1971) pointed out a difference in the sutures of the posterior parts of the premaxillary and nasal bones compared to the frontal one, but this criterion does not work well in many cases. For both paleontological and biogeographical research it would be useful to have a good rule for discriminating between the two species, because much of the data available are in form of skull remains, either fossilized or from owl pellets. The present study was initiated by a data collection consisting of eight morphometric variables measured by one of the authors (Salvioni) using a Nikon measure-scope (accuracy 1/1000 mm) and dial calipers (accuracy 1/100 mm).

The sample consists of 288 specimens collected mostly in Central Europe (Alps and Jura mountains) and in Toscana. One peculiar aspect of this data set is that the chromosomes of 89 specimens were analyzed to identify the species. Only the morphometric characteristics are available for the remaining 199 specimens.

Develop a generalized linear model from the 89 specimens that you can use to predict the group membership of the remaining 199 specimens.

a. Explain your GLM and assess the quality of the fit with the classified observations. Use Cross Validation to predict the accuracy of your model.

b. Provide a one-page write-up (including graphs) explaining your analysis of the dataset and your recommendations on the usefulness of your predictions.

c. Provide predictions for the unclassified observations.

d. As a secondary component provide annotated code that replicates your analysis.

Only Question 2 and 3 needs to be done.