Factor copula models for mixed data

We develop factor copula models to analyse the dependence among mixed continuous and discrete responses. Factor copula models are canonical vine copulas that involve both observed and latent variables, hence they allow tail, asymmetric and nonlinear dependence. They can be explained as conditional independence models with latent variables that do not necessarily have an additive latent structure. We focus on important issues of interest to the social data analyst, such as model selection and goodness of fit. Our general methodology is demonstrated with an extensive simulation study and illustrated by reanalysing three mixed response data sets. Our studies suggest that there can be a substantial improvement over the standard factor model for mixed data and make the argument for moving to factor copula models.     

The effects of phencyclidine and chlordiazepoxide on target biting of confined male mice

Target-biting of confined mice increases following delivery of tail shock and decreases during a tone that precedes the shock. Both phencyclidine and chlordiazepoxide reduced biting (dose dependently) following shock and had no effect on biting during the tone. These observations are discussed in reference to previous reports, which infer that the effects of phencyclidine and chlordiazepoxide on aggression might depend upon the baseline rate of the behavior.     

On the exponent in the "generalized" matching equation

A power function equation between ratios of behavior and ratios of reinforcement rates has been called a generalized form of Herrnstein's (1961) matching law, even without a formal relationship having been shown between the two equations. The present work uses a functional relationship to prove that when ratios of reinforcement are not equivalent to ratios of behavior, and the transform leading to this inequality is consistent for every pair of reinforcement rates, the result is a power function relationship between response and reinforcement ratios. The label “generalized matching equation” for the power function equation is thus validated formally.     

Control of the temporal locations of polydipsic licking in the rat.

We studied the variables controlling the temporal location of polydipsic licking. Four rats were trained on a mixed fixed-ratio 10 (no tone) chained fixed-ratio 10 (no tone) fixed-ratio 90 (tone) schedule and on a multiple fixed-ratio 10 (tone) fixed ratio 100 (no tone) schedule. On the multiple schedule, drinking followed pellets if a fixed ratio 100 was upcoming for all four subjects and for two of the subjects if a fixed ratio 10 was upcoming. On the mixed schedule, drinking preceded the fixed-ratio 90 component of the chain. Two subjects also drank after pellet delivery on the mixed schedule before both the fixed ration 10 and the chain components. The number of licks was greater following a pellet than following a response. In a second phase with two of these subjects, the total response requirement of the chain was held constant at 100, while the size of the two ratios that constituted the chain was varied inversely. The tone signaled onset of the second link. Drinking followed the tone when it signaled fixed-ratio 90, 95, or 100 but not when it signaled fixed ratio 75, 80, or 85. These results show, on the one hand, that polydipsic licking is controlled by discriminative properties of the pellet rather than by its eliciting or "thirst-producing" characteristics. On the other hand, the fact that drinks were longer following a pellet than following a response suggests a contribution of thirst to polydipsia.     

The effects of tail shock on target-biting behavior of confined mice

Mice that are confined in a narrow cylinder readily bite inanimate targets. The following studies were conducted to determine the effects of tail shock on the target biting behavior of two strains of mice. During 20-min daily sessions, ten tail shocks were administered on a fixed-time 2-min schedule. One group of mice received a tone-conditioned stimulus (CS) which terminated with the onset of the shock, and a second group of mice did not. Target bites were collected in eight 15-sec bins over the 2-min trial and cumulated over the session. It was observed that tail shock was followed by an increase in target biting and that there was a comparatively high intershock interval biting rate. In addition, intershock interval biting was suppressed for the duration of the CS. These observations are discussed in terms of the utility of this paradigm for the psychopharmacological assessment of aggressive behavior.     

Multivariate normal integrals and contingency tables with ordered categories

Ak-dimensional multivariate normal distribution is made discrete by partitioning thek-dimensional Euclidean space with rectangular grids. The collection of probability integrals over the partitioned cubes is ak-dimensional contingency table with ordered categories. It is shown that loglinear model with main effects plus two-way interactions provides an accurate approximation for thek-dimensional table. The complete multivariate normal integral table is computed via the iterative proportional fitting algorithm from bivariate normal integral tables. This approach imposes no restriction on the correlation matrix. Comparisons with other numerical integration algorithms are reported. The approximation suggests association models for discretized multivariate normal distributions and contingency tables with ordered categories.The contingency-table approach occurred to me while I was collaborating with Paul Holland of the Educational Testing Service in 1985 on bivariate dependence functions. Holland maintains a belief that the continuous can learn from the discrete. This work is a reassertion of his claim.This research was sponsored by the National Science Council, Republic of China.     

Sample-specific ratio effects in matching to sample

In a symbolic matching-to-sample task, pigeons were trained using sample-specific, fixed-ratio “observing responses.” Subsequently, in a mixed condition, each sample was presented equally often with each ratio requirement, i.e., the ratios were no longer correlated with the samples. In a second experiment, pigeons were trained initially in the mixed condition and subsequently shifted to the sample-specific condition in which the required ratios were correlated with the samples. Results of both experiments suggested joint control of choices by ratio value and by the exteroceptive stimuli. The discriminative properties of the ratios appeared to outweigh absolute ratio-size effects.