Discrimination learning in a foraging situation

Rats were allowed to forage in a simulated natural environment made up of eight food sources (patches) each containing a fixed number of pellets. Two of the eight contained an extra supply of peanuts. The peanut patches were signaled by an olfactory/visual cue located at the bottom of the ladder leading to the patch. In successive phases the number of sessions per day, height of the patches, and availability of peanuts were manipulated. Subjects showed evidence of discrimination learning under these conditions, although the degree of discriminatory behavior varied as a function of environmental manipulations. Assessment of behavior within foraging sessions showed that subjects systematically changed their patterns of utilization of patches across time. Sampling or exploration, as well as food reinforcement, seem implicated in these results.     

Canonical analysis of two convex polyhedral cones and applications

Canonical analysis of two convex polyhedral cones consists in looking for two vectors (one in each cone) whose square cosine is a maximum. This paper presents new results about the properties of the optimal solution to this problem, and also discusses in detail the convergence of an alternating least squares algorithm. The set of scalings of an ordinal variable is a convex polyhedral cone, which thus plays an important role in optimal scaling methods for the analysis of ordinal data. Monotone analysis of variance, and correspondence analysis subject to an ordinal constraint on one of the factors are both canonical analyses of a convex polyhedral cone and a subspace. Optimal multiple regression of a dependent ordinal variable on a set of independent ordinal variables is a canonical analysis of two convex polyhedral cones as long as the signs of the regression coefficients are given. We discuss these three situations and illustrate them by examples.     

Time-place learning by pigeons, Columba livia

In each of two experiments, 2 pigeons received discrimination training in which food reinforcement for key pecking was conditional upon both spatial and temporal cues. In Experiment 1, food was available for periods of 30 s at each of three locations (pecking keys) during trials that lasted 90 s. In Experiment 2, food was available for periods of 15 min at each of four locations (pecking keys) during a 60-min trial. In both experiments, pigeons' key pecking was jointly controlled by the spatial and temporal cues. These data, and other recent experiments, suggest that animals learn relationships between temporal and spatial cues that predict stable patterns of food availability.     

Imputation of missing categorical data by maximizing internal consistency

This paper suggests a method to supplant missing categorical data by reasonable replacements. These replacements will maximize the consistency of the completed data as measured by Guttman's squared correlation ratio. The text outlines a solution of the optimization problem, describes relationships with the relevant psychometric theory, and studies some properties of the method in detail. The main result is that the average correlation should be at least 0.50 before the method becomes practical. At that point, the technique gives reasonable results up to 10–15% missing data.We thank Anneke Bloemhoff of NIPG-TNO for compiling and making the Dutch Life Style Survey data available to use, and Chantal Houée and Thérèse Bardaine, IUT, Vannes, France, exchange students under the COMETT program of the EC, for computational assistance. We also thank Donald Rubin, the Editors and several anonymous reviewers for constructive suggestions.     

Handling time and choice in pigeons

According to optimal foraging theory, animals should prefer food items with the highest ratios of energy intake to handling time. When single items have negligible handling times, one large item should be preferred to a collection of small ones of equivalent total weight. However, when pigeons were offered such a choice on equal concurrent variable-interval schedules in a shuttlebox, they preferred the side offering many small items per reinforcement to that offering one or a few relatively large items. This preference was still evident on concurrent fixed-cumulative-duration schedules in which choosing the alternative with longer handling time substantially lowered the rate of food intake.     

The choice of constraints in correspondence analysis

A discussion of alternative constraint systems has been lacking in the literature on correspondence analysis and related techniques. This paper reiterates earlier results that an explicit choice of constraints has to be made which can have important effects on the resulting scores. The paper also presents new results on dealing with missing data and probabilistic category assignment.I am most grateful to the following for their helpful comments. Arto Demirjian, Michael Greenacre, Michael Healy, Shizuhiko Nishisato, Roderick Mcdonald, and several anonymous referees.     

The matching law applies to wagtails' foraging in the wild

Field data concerning the time budgets and foraging success of pied wagtails (Motacilla alba yarrelli, Gould) are reanalyzed. It is found that the data are well described by the generalized matching law, with a marked bias towards spending time on the territory. In this case matching is not the result of maximizing reward rate, but it remains possible that it results from an allocation of time that maximizes survival.     

A temporal limit on the effect of future food on current performance in an analogue of foraging and welfare

Rats obtained access to food twice each 24-hour period. The first session was a work session in which food was available on a progressive-ratio schedule. During the second session, which occurred between 1 and 23 hours after the work session, food was freely available up to a fixed total intake each 24 hours. The situation resembled elements of several real world circumstances, including the choice between continuing to forage in a rapidly depleting patch and waiting for a better patch, and between working now and receiving a guaranteed income later. The purpose of the experiment was to explore the time period over which future access to reward could affect current responding. Contrary to what might be expected from recent theorizing, anticipation of future food delayed by an hour or more after the start of the work session had no effect on current performance. Food intake was high and constant during work sessions except for a prefeeding effect that occurred when the free session closely preceded the next day's work session. Also, an increase in the difficulty of the work schedule increased the amount of work and the maximum price paid for food as if the work session were the only time food was available. The results indicate the importance of considering temporal limits in theories that require animals to integrate input over time to determine the allocation of resources among alternatives.     

Redundancy analysis for qualitative variables

Redundancy analysis (also called principal components analysis of instrumental variables) is a technique for two sets of variables, one set being dependent of the other. Its aim is maximization of the explained variance of the dependent variables by a linear combination of the explanatory variables. The technique is generalized to qualitative variables; it then gives implicitly a simultaneous optimal scaling of the dependent, qualitative variables. Examples are taken from the Dutch Life Situation Survey 1977, using Satisfaction with Life and Happiness as dependent variables. The analysis leads to one well-being scale, defined by the explanatory variables Marital status, Schooling, Income and Activity.The views expressed in this paper are those of the author and do not necessarily reflect the policies of the Netherlands Central Bureau of Statistics.     

Penalized optimal scaling for ordinal variables with an application to international classification of functioning core sets

Ordinal data occur frequently in the social sciences. When applying principal component analysis (PCA), however, those data are often treated as numeric, implying linear relationships between the variables at hand; alternatively, non-linear PCA is applied where the obtained quantifications are sometimes hard to interpret. Non-linear PCA for categorical data, also called optimal scoring/scaling, constructs new variables by assigning numerical values to categories such that the proportion of variance in those new variables that is explained by a predefined number of principal components (PCs) is maximized. We propose a penalized version of non-linear PCA for ordinal variables that is a smoothed intermediate between standard PCA on category labels and non-linear PCA as used so far. The new approach is by no means limited to monotonic effects and offers both better interpretability of the non-linear transformation of the category labels and better performance on validation data than unpenalized non-linear PCA and/or standard linear PCA. In particular, an application of penalized optimal scaling to ordinal data as given with the International Classification of Functioning, Disability and Health (ICF) is provided.