A unified approach to exploratory factor analysis with missing data,nonnormal data,and in the presence of outliers

Factor analysis is regularly used for analyzing survey data. Missing data, data with outliers and consequently nonnormal data are very common for data obtained through questionnaires. Based on covariance matrix estimates for such nonstandard samples, a unified approach for factor analysis is developed. By generalizing the approach of maximum likelihood under constraints, statistical properties of the estimates for factor loadings and error variances are obtained. A rescaled Bartlett-corrected statistic is proposed for evaluating the number of factors. Equivariance and invariance of parameter estimates and their standard errors for canonical, varimax, and normalized varimax rotations are discussed. Numerical results illustrate the sensitivity of classical methods and advantages of the proposed procedures.This project was supported by a University of North Texas Faculty Research Grant, Grant #R49/CCR610528 for Disease Control and Prevention from the National Center for Injury Prevention and Control, and Grant DA01070 from the National Institute on Drug Abuse. The results do not necessarily represent the official view of the funding agencies. The authors are grateful to three reviewers for suggestions that improved the presentation of this paper.     

Progressive-ratio schedules: effects of later schedule requirements on earlier performances

Four rats were studied with variants of a progressive-ratio schedule with a step size of 6 in which different terminal components followed completion of the 20th ratio: (a) a reversal of the progression, (b) a fixed-ratio 6 schedule, or (c) extinction. Responding in the progressive-ratio components of these schedules was compared to performances under conventional progressive-ratio baselines. Under baseline conditions, postreinforcement pauses increased exponentially as a function of increasing ratio size, whereas running rates showed modest declines. The procedure of linking the progressive-ratio schedule to the reversed progression or to the fixed-ratio component resulted in decreased pausing. Linking the progressive-ratio schedule to the extinction component had the opposite effect, that of producing weakened progressive-ratio performances as evidenced by increased pausing. Subjects whose responses were reinforced on half of the ratios also showed exponential increases; however, pauses were substantially shorter following ratios on which the reinforcer was omitted. The results suggested that progressive-ratio pausing reflects the influence of remote as well as local contingencies.     

MORPHINE TOLERANCE AS A FUNCTION OF RATIO SCHEDULE: RESPONSE REQUIREMENT OR UNIT PRICE?

Key pecking by 3 pigeons was maintained by a multiple fixed-ratio 10, fixed-ratio 30, fixed-ratio 90 schedule of food presentation. Components differed with respect to amount of reinforcement, such that the unit price was 10 responses per 1-s access to food. Acute administration of morphine, l-methadone, and cocaine dose-dependently decreased overall response rates in each of the components. When a rate decreasing dose of morphine was administered daily, tolerance, as measured by an increase in the dose that reduced response rates to 50% of control (i.e., the ED50 value), developed in each of the components; however, the degree of tolerance was smallest in the fixed-ratio 90 component (i.e., the ED50 value increased the least). When the l-methadone dose-effect curve was redetermined during the chronic morphine phase, the degree of cross-tolerance conferred to l-methadone was similar across components, suggesting that behavioral variables may not influence the degree of cross-tolerance between opioids. During the chronic phase, the cocaine dose-effect curve shifted to the right for 2 pigeons and to the left for 1 pigeon, which is consistent with predictions based on the lack of pharmacological similarity between morphine and cocaine. When the morphine, l-methadone, and cocaine dose-effect curves were redetermined after chronic morphine administration ended, the morphine and l-methadone ED50s replicated those obtained prior to chronic morphine administration. The morphine data suggest that the fixed-ratio value (i.e., the absolute output) determines the degree of tolerance and not the unit price.     

Female physical attractiveness in Britain and Malaysia: a cross-cultural study

Two purported cues to perceived female physical attractiveness are body mass index (BMI) and body shape as measured by the waist-to-hip ratio (WHR). This study examined the relative contribution of both cues in several culturally socio-economically distinct populations. Six hundred and eighty-two participants from Britain and Malaysia were asked to rate a set of images of real women with known BMI and WHR. The results showed that BMI is the primary determinant of female physical attractiveness, whereas WHR failed to emerge as a significant predictor. The results also showed that there were significant differences in preferences for physical attractiveness along a gradient of socio-economic development, with urban participants preferring images of women with significantly lower BMIs than their rural counterparts. The findings are discussed in terms of evolutionary psychological explanations of mate selection, and sociocultural theory, which emphasises the learning of preferences for body sizes in social and cultural contexts.     

Effects of anorectic drugs on food intake under progressive-ratio and free-access conditions in rats

The effects of two anorectic drugs, dexfenfluramine and phentermine, on food intake under different food-access conditions were examined. Experiment 1 compared the effects of these drugs on food intake under a progressive-ratio (PR) schedule and free-access conditions. Dexfenfluramine decreased food intake under both conditions, but the doses required to decrease intake under free-access conditions were higher than those required to reduce intake under the PR condition. Intermediate doses of phentermine sometimes increased breaking points, and higher doses decreased them. Phentermine decreased food intake at the same doses under both access conditions. Thus the potency of dexfenfluramine, but not phentermine, to decrease food-maintained behavior depended upon the food-access condition. Experiment 2 used a novel mixed progressive-ratio schedule of food delivery to study the duration of drug effects. Sessions consisted of five components separated by 3-hr timeouts. The ratio requirement reset at the beginning of each component and a new breaking point was obtained. Both dexfenfluramine and phentermine dose-dependently decreased breaking points early in the session. In some rats, compensatory increases in breaking point were observed. That is, breaking points later in the session increased over control levels, resulting in no change in the total number of food pellets earned for the session compared to control. The present findings suggest that the effects of some anorectic drugs depend upon the access conditions for food; increasing the effort to obtain food may enhance their ability to decrease food-maintained behavior.     

Second-order schedules of token reinforcement with pigeons: effects of fixed- and variable-ratio exchange schedules

Pigeons' key pecks produced food under second-order schedules of token reinforcement, with light-emitting diodes serving as token reinforcers. In Experiment 1, tokens were earned according to a fixed-ratio 50 schedule and were exchanged for food according to either fixed-ratio or variable-ratio exchange schedules, with schedule type varied across conditions. In Experiment 2, schedule type was varied within sessions using a multiple schedule. In one component, tokens were earned according to a fixed-ratio 50 schedule and exchanged according to a variable-ratio schedule. In the other component, tokens were earned according to a variable-ratio 50 schedule and exchanged according to a fixed-ratio schedule. In both experiments, the number of responses per exchange was varied parametrically across conditions, ranging from 50 to 400 responses. Response rates decreased systematically with increases in the fixed-ratio exchange schedules, but were much less affected by changes in the variable-ratio exchange schedules. Response rates were consistently higher under variable-ratio exchange schedules than tinder comparable fixed-ratio exchange schedules, especially at higher exchange ratios. These response-rate differences were due both to greater pre-ratio pausing and to lower local rates tinder the fixed-ratio exchange schedules. Local response rates increased with proximity to food under the higher fixed-ratio exchange schedules, indicative of discriminative control by the tokens.     

The long-term effect of high- and low-rate responding histories on fixed-interval responding in rats

Tell rats were given extended lever-press training on a fixed-interval (FI) 30-s food reinforcement schedule from the outset or following exposure to one or two previous reinforcement schedules. For 4 rats the previots schedule was either fixed-ratio 20, which generated high response rates, or differential-reinforcement-of-low-rate 20 s, which produced low response rates. For 4 additional rats the extended training on FI 30 s was preceded by experience with two schedules: fixed-ratio 20 followed by differential-reinforcement-of-low-rate 20 s; or the same two schedules in the reverse order. Fixed-interval response rates were initially affected by the immediately preceding schedule, but after 80 to 100 sessions, all traces of prior schedule history had disappeared. The results also showed no long-term effect of schedule history on the interfood-interval patterns of responding on the FI 30-s schedule. These results support one of the most central tenets of the experimental analysis of behavior: control by the immediate consequences of behavior.     

Behavioral and pharmacological variables affecting risky choice in rats.

The effects of manipulations of response requirement, intertrial interval (ITI), and psychoactive drugs (ethanol, phencyclidine, and d-amphetamine) on lever choice under concurrent fixed-ratio schedules were investigated in rats. Responding on the "certain' lever produced three 45-mg pellets, whereas responding on the "risky" lever produced either 15 pellets (p = .33) or no pellets (p .67). Rats earned all food during the session, which ended after 12 forced trials and 93 choice trials or 90 min, whichever occurred first. When the response requirement was increased from 1 to 16 and the ITI was 20 s, percentage of risky choice was inversely related to fixed-ratio value. When only a single response was required but the ITI was manipulated between 20 and 120 s (with maximum session duration held constant), percentage of risky choice was directly related to length of the ITI. The effects of the drugs were investigated first at an ITI of 20 s, when risky choice was low for most rats, and then at an ITI of 80 s, when risky choice was higher for most rats. Ethanol usually decreased risky choice. Phencyclidine did not usually affect risky choice when the ITI was 20 s but decreased it in half the rats when the ITI was 80 s. For d-amphetamine, the effects appeared to he related to baseline probability of risky choice; that is, low probabilities were increased and high probabilities were decreased. Although increase in risky choice as a function of the ITI is at variance with previous ITI data, it is consistent with foraging data showing that risk aversion decreases as food availability decreases. The pharmacological manipulations showed that drug effects on risky choice may be influenced by the baseline probability of risky choice, just as drug effects can be a function of baseline response rate.     

Food and cocaine self-administration by baboons: effects of alternatives.

The effects of the availability of an alternative reinforcer on responding maintained by food pellets or drug solutions were examined in 8 adult male baboons (Papio hamadrayas anubis). During daily 23-hr experimental sessions, baboons had access to both food pellets and fluid under a two-choice procedure, in which the response requirement, under a fixed-ratio schedule, differed for the two commodities. There were no restrictions on access to water, which was continuously available from a spout at the rear of each cage. In Experiment 1, the fixed-ratio requirement, or cost, for fluid delivery remained constant while the fixed-ratio requirement for pellets was changed every 2 or 3 days when (a) no fluid, (b) a dilute dextrose vehicle, (c) 0.008 mg/kg per delivery cocaine, (d) 0.016 mg/kg per delivery cocaine, or (e) 0.032 mg/kg per delivery cocaine was available concurrently. In Experiment 1, progressively increasing the response requirement for pellets decreased pellet intake, but for 4 baboons pellet intake at maximum pellet cost was lower when cocaine, compared to the vehicle, was available. Increasing the response requirement for pellets had variable effects on vehicle intake. However, increasing the response requirement for pellets increased intake of at least one dose of cocaine to a greater extent than vehicle in all 8 baboons. Thus, cocaine could be considered a more effective economic substitute than vehicle for pellets. Experiment 2 systematically varied the order in which the response requirements for a pellet delivery were presented and added a control condition in which cocaine doses, yoked to the amount self-administered, were given three times during the session by the experimenter. Again, pellet intake at maximal pellet cost was lower when cocaine, compared to the vehicle, was available. In contrast, experimenter-given cocaine doses did not alter responding maintained by pellets. Thus, the effects of self-administered cocaine on responding maintained by food pellets differed from the effects of experimenter-given cocaine on responding maintained by food pellets.     

How Long Do Offenders Escape Arrest? Using DNA Traces to Analyse when Serial Offenders Are Caught

Why is it that some serial offenders are arrested quickly and others only after a long period, or never at all? What characterises offenders who continue to escape arrest despite their continued involvement in crime? To be able to answer these questions, arrested (identified) offenders must be compared with never arrested (unidentified) offenders. In this paper, data from the Dutch DNA database are used to assess which characteristics of the criminal behaviour of unidentified offenders influence the probability that they will subsequently be arrested. DNA data offer a unique opportunity to compare crime series of identified offenders with crime series of yet unidentified offenders. Using the Cox proportional hazards model, we tested whether the number of crimes committed, offence specialization, and offence seriousness affect the probability of arrest of serial offenders. Results showed that as an offender commits more crimes, the probability that he will be arrested increases and that offence specialization decreases the probability of arrest. Another conclusion drawn is that DNA traces offer unique opportunities for criminological research. We discuss the limitations of this new data source and make suggestions for future research using DNA traces and for future research that might improve the current study. Copyright © 2012 John Wiley & Sons, Ltd.