Multiple correspondence analysis of a subset of response categories

In the analysis of multivariate categorical data, typically the analysis of questionnaire data, it is often advantageous, for substantive and technical reasons, to analyse a subset of response categories. In multiple correspondence analysis, where each category is coded as a column of an indicator matrix or row and column of Burt matrix, it is not correct to simply analyse the corresponding submatrix of data, since the whole geometric structure is different for the submatrix . A simple modification of the correspondence analysis algorithm allows the overall geometric structure of the complete data set to be retained while calculating the solution for the selected subset of points. This strategy is useful for analysing patterns of response amongst any subset of categories and relating these patterns to demographic factors, especially for studying patterns of particular responses such as missing and neutral responses. The methodology is illustrated using data from the International Social Survey Program on Family and Changing Gender Roles in 1994.Categorical data, correspondence analysis, questionnaire survey

Subset correspondence analysis: Visualizing relationships among a selected set of response categories from a questionnaire survey

It is shown how correspondence analysis may be applied to a subset of response categories from a questionnaire survey, for example the subset of undecided responses or the subset of responses for a particular category. The idea is to maintain the original relative frequencies of the categories and not re-express them relative to totals within the subset, as would normally be done in a regular correspondence analysis of the subset. Furthermore, the masses and chi-square metric assigned to the data subset are the same as those in the correspondence analysis of the whole data set. This variant of the method, called Subset Correspondence Analysis, is illustrated on data from the ISSP survey on Family and Changing Gender Roles.Categorical data, correspondence analysis, questionnaire survey

Group Agency and Legal Proof; or, Why the Jury Is an “It”

Jurors decide whether certain facts have been proven according to the applicable legal standards. What is the relationship between the jury, as a collective decision-making body, on one hand, and the views of individual jurors, on the other? Is the jury merely the sum total of the individual views of its members? Or do juries possess properties and characteristics of agency (for example, beliefs, knowledge, preferences, intentions, plans, and actions) that are in some sense distinct from those of its members? This Article explores these questions and defends a conception of the jury as a group agent with agency that may differ from that of its members. The Article then argues that this conception of the jury contains important implications for law and legal proof. These implications are both theoretical and practical. On the theoretical side, recent debates in evidence law have focused on whether legal proof is probabilistic or explanatory in nature. These debates, however, have largely assumed a single, unified fact-finder (whether jury or judge). The group-level perspective reveals new conceptual problems for the probabilistic theory that are alleviated by the explanatory theory; it thus provides further vindication for the explanatory account. On the practical side, the conception of the jury as a group agent, coupled with the explanatory account of proof, clarifies doctrinal issues on whether, and when, jurors must agree on factual details. In both criminal and civil cases, these issues have caused considerable confusion and uncertainty for courts and commentators

Pleadings, Proof, and Judgment: A Unifed Theory of Civil Litigation

The U.S. Supreme Court’s recent pleadings decisions—Bell Atlantic Corp. v. Twombly and Ashcroft v. Iqbal—have injected considerable chaos into the system of civil litigation. The decisions impose an uncertain “plausibility” requirement and appear to endorse an increased power of district courts to dismiss complaints—a power that may be employed in an unprincipled, normatively problematic manner. The current pleading issues resemble similar issues that have arisen with summary judgment and judgment as a matter of law. This Article argues that there has been a significant failure at both the doctrinal and theoretical levels to relate these three procedural devices to the evidentiary proof process in particular and the system of civil litigation as a whole. It introduces a theory of “procedural accuracy” that explains, clarifies, and provides content to the standards for each device, explains how the theory fits, and explains important aspects of the doctrine for each device. Finally, and most importantly, I defend the theory and its standards as normatively desirable in light of procedural values that underlie the system of civil litigation as a whole

Tail Communication in the Eastern Gray Squirrel, Sciurus carolinensis

Tree squirrels are known to communicate with their tails, but the only aspects of this communication that have been studied are tail flicking and piloerection. I investigated the communicative significance of tail position in wild eastern gray squirrels by videotaping them at an artificial food source. For each individual, I recorded dominance rank, aggression, avoidance behavior, and three variables describing tail position (tightness of curvature, portion of tail bent, and tail contact with ground). When a subordinate squirrel approached a dominant squirrel I recorded whether the approach was successful, and when a dominant squirrel approached a subordinate squirrel I recorded the distance that the subordinate moved away. All three tail position variables were correlated with the behavior of both the signaler and the receiver. The interaction effect between the tail positions of two interacting squirrels was a better predictor of the more dominant squirrel’s degree of aggression than either squirrel’s tail position alone. Analysis suggested that different tail variables do not communicate the same information, indicating that tail position may communicate multiple pieces of information simultaneously. I hypothesize that the tightness of the tail’s curvature communicates a squirrel’s degree of confidence (its status), the portion of the tail that is bent communicates degree of hunger, and whether the tail is touching the ground indicates intent to move