A Monte Carlo evaluation of three formula estimates of cross-validated multiple correlation.

To determine the stability of regression equations, researchers have typically employed a cross-validation design in which weights are developed on an estimation subset of the sample and then applied to the members of a holdout sample. The present study used a Monte Carlo simulation to ascertain the accuracy with which the shrinkage in R–2 could be estimated by 3 formulas developed for this purpose. Results indicate that R. B. Darlington's (see record 1968-08053-001) and F. M. Lord (1950) and G. E. Nicholson's (1960) formulas yielded mean estimates approximately equal to actual cross-validation values, but with smaller standard errors. Although the Wherry estimate is a good estimate of population multiple correlation, it is an overestimate on population cross-validity. It is advised that the researcher estimate weights on the total sample to maximize the stability of the regression equation and then estimate the shrinkage in R–2 that he/she can expect when going to a new sample with either the Lord-Nicholson or Darlington estimation formulas. (17 ref) (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Bootstrap Standard Error and Confidence Intervals for the Correlation Corrected for Range Restriction: A Simulation Study.

The standard Pearson correlation coefficient is a biased estimator of the true population correlation, ρ, when the predictor and the criterion are range restricted. To correct the bias, the correlation corrected for range restriction, rc, has been recommended, and a standard formula based on asymptotic results for estimating its standard error is also available. In the present study, the bootstrap standard-error estimate is proposed as an alternative. Monte Carlo simulation studies involving both normal and nonnormal data were conducted to examine the empirical performance of the proposed procedure under different levels of ρ, selection ratio, sample size, and truncation types. Results indicated that, with normal data, the bootstrap standard-error estimate is more accurate than the traditional estimate, particularly with small sample size. With nonnormal data, performance of both estimates depends critically on the distribution type. Furthermore, the bootstrap bias-corrected and accelerated interval consistently provided the most accurate coverage probability for ρ. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Human judgment and estimation of premorbid intellectual function.

Examined clinical judgment in estimating premorbid intellectual function (IQ). In 2 experiments, clinical neuropsychologists were asked to (1) specify their beliefs about the interrelationships between IQ and demographic predictors and (2) estimate IQ scores for hypothetical individuals. The clinicians believed that the relationships between the variables were stronger than previous research has established. On the judgment tasks, the clinicians provided narrower confidence intervals than those derived from their beliefs about the correlations, although this effect was primarily limited to estimates of Performance IQ. There were also discrepancies between clinicians' beliefs about the IQ–predictor correlations and the correlations between the clinicians' IQ estimates and the same predictors, suggesting inability to appropriately regress estimates. Although the clinicians' IQ estimates were close to those of an actuarial formula using the same information, their confidence was considerably higher. Constraints on human reasoning and memory disable clinical reasoners from making estimates of premorbid IQ that reflect the predictive power of demographic variables. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Analytical considerations in the use of capture-recapture to estimate prevalence: case studies of the estimation of opiate use in the metropolitan area of Barcelona, Spain

Capture-recapture, an indirect method widely used to estimate undetected populations, has been criticized because it causes problems due to a lack of compliance with several important assumptions and model selection strategies. This paper expands on the problems encountered when applying this methodology to drug abuse estimations, specifically the prevalence of opiate use in the metropolitan area of Barcelona, Spain, in 1993. Three samples of opiate users (from hospital emergency rooms, treatment centers, and prisons) were available in the area studied; an additional sample (mortality data) was analyzed for the city of Barcelona. Log-linear models that provided a good fit were considered, to which further model selection strategies were applied. A total of 3,207 unique individuals aged 15-44 years were identified in the three samples from the greater Barcelona area; the mortality sample from the city of Barcelona contained an additional 83 individuals. Heterogeneity was observed in different age, sex, and residence area subgroups. Population estimates differed widely according to the log-linear model chosen. Minimum Akaike's information criterion model and saturated model estimates were used to produce population prevalence rates. The main problems the authors encountered in this study were related to population definition, source heterogeneity, and assessment of an adequate model, a problem associated with sample size.     

Sample Size for Multiple Regression: Obtaining Regression Coefficients That Are Accurate, Not Simply Significant.

An approach to sample size planning for multiple regression is presented that emphasizes accuracy in parameter estimation (AIPE). The AIPE approach yields precise estimates of population parameters by providing necessary sample sizes in order for the likely widths of confidence intervals to be sufficiently narrow. One AIPE method yields a sample size such that the expected width of the confidence interval around the standardized population regression coefficient is equal to the width specified. An enhanced formulation ensures, with some stipulated probability, that the width of the confidence interval will be no larger than the width specified. Issues involving standardized regression coefficients and random predictors are discussed, as are the philosophical differences between AIPE and the power analytic approaches to sample size planning. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Estimating test norms via multiple matrix sampling.

Compared estimates of a population mean and variance obtained by examinee sampling and multiple matrix sampling (MMS), using a computer-simulated database. Variables were number of observations and item subtest sizes. Results indicate that MMS provided as good estimates of a population mean and variance as examinee sampling. The estimate of population variance, however, became more stable as number of items in each subtest increased. (French abstract) (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

A procedure for combining sample correlation coefficients and vote counts to obtain an estimate and a confidence interval for the population correlation coefficient.

Missing effect-size estimates pose a particularly difficult problem in meta-analysis. Rather than discarding studies with missing effect-size estimates or setting missing effect-size estimates equal to 0, the meta-analyst can supplement effect-size procedures with vote-counting procedures if the studies report the direction of results or the statistical significance of results. By combining effect-size and vote-counting procedures, the meta-analyst can obtain a less biased estimate of the population effect size and a narrower confidence interval for the population effect size. This article describes 3 vote-counting procedures for estimating the population correlation coefficient in studies with missing sample correlations. Easy-to-use tables, based on equal sample sizes, are presented for the 3 procedures. More complicated vote-counting procedures also are given for unequal sample sizes. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Asymptotically distribution-free (ADF) interval estimation of coefficient alpha.

[Correction Notice: An erratum for this article was reported in Vol 12(4) of Psychological Methods (see record 2007-18729-004). The sentence describing Equation 1 is incorrect. The corrected sentence is presented in the erratum.] The point estimate of sample coefficient alpha may provide a misleading impression of the reliability of the test score. Because sample coefficient alpha is consistently biased downward, it is more likely to yield a misleading impression of poor reliability. The magnitude of the bias is greatest precisely when the variability of sample alpha is greatest (small population reliability and small sample size). Taking into account the variability of sample alpha with an interval estimator may lead to retaining reliable tests that would be otherwise rejected. Here, the authors performed simulation studies to investigate the behavior of asymptotically distribution-free (ADF) versus normal-theory interval estimators of coefficient alpha under varied conditions. Normal-theory intervals were found to be less accurate when item skewness >1 or excess kurtosis >1. For sample sizes over 100 observations, ADF intervals are preferable, regardless of item skewness and kurtosis. A formula for computing ADF confidence intervals for coefficient alpha for tests of any size is provided, along with its implementation as an SAS macro. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Inheritance of teat number and its relationship to maternal traits in swine

The relationship of teat number to seven measures of female reproduction was evaluated in the University of Nebraska Gene Pool population. Teat number was recorded for 7,513 pigs, ovulation rate for 2,794 gilts and litter size and weight at birth and weaning (42 days) for 789 gilts. Paternal half-sib and full-sib analyses were used to estimate heritabilities for each trait and to estimate the genetic and phenotypic correlations of teat number with the measures of reproduction. The direct response to selection for ovulation rate and the correlated response in teat number were also evaluated from the regressions of line differences (Select-Control) on generation number (10 generations of selection) and cumulative selection differential for ovulation rate. The paternal half-sib heritabililty for teat number was .32, and the paternal half-sib heritabilities for ovulation rate and the litter traits were similar to previous estimates from this population. Most of the genetic and phenotypic correlations with teat number were negative and all were nonsignificant. The realized heritability for ovulation rate was .46 +/- .10. The regression of response in teat number on generation number number was .08 +/- .03 (P < .10). An estimate of .44 was obtained for the realized genetic correlation of teat number with ovulation rate.     

Population diversity: its extent and extinction

Genetically distinct populations are an important component of biodiversity. This work estimates the number of populations per area of a sample of species from literature on population differentiation and the average range area of a species from a sample of distribution maps. This yields an estimate of about 220 populations per species, or 1.1 to 6.6 billion populations globally. Assuming that population extinction is a linear function of habitat loss, approximately 1800 populations per hour (16 million annually) are being destroyed in tropical forests alone.     

requivalent: A Simple Effect Size Indicator.

The purpose of this article is to propose a simple effect size estimate (obtained from the sample size, N, and a p value) that can be used (a) in meta-analytic research where only sample sizes and p values have been reported by the original investigator, (b) where no generally accepted effect size estimate exists, or (c) where directly computed effect size estimates are likely to be misleading. This effect size estimate is called requivalent because it equals the sample point-biserial correlation between the treatment indicator and an exactly normally distributed outcome in a two-treatment experiment with N/2 units in each group and the obtained p value. As part of placing requlvaient into a broader context, the authors also address limitations of requivalent. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

A computer readability formula designed for machine scoring.

Existing computer programs that measure readability are based largely upon subroutines which estimate number of syllables, usually by counting vowels. The shortcoming in estimating syllables is that it necessitates keypunching the prose into the computer. There is no need to estimate syllables since word length in letters is a better predictor of readability than word length in syllables. Therefore, a new readability formula was computed that has for its predictors letters per 100 words and sentences per 100 words. Both predictors can be counted by an optical scanning device, and thus the formula makes it economically feasible for an organization (e.g., the US Office of Education) to calibrate the readability of all textbooks for the public school system. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

"Asymptotically distribution-free (ADF) interval estimation of coefficient alpha": Correction.

Reports an error in "Asymptotically distribution-free (ADF) interval estimation of coefficient alpha" by Alberto Maydeu-Olivares, Donna L. Coffman and Wolfgang M. Hartmann (Psychological Methods, 2007[Jun], Vol 12[2], 157-176). The sentence describing Equation 1 is incorrect. The corrected sentence is presented in the erratum. (The following abstract of the original article appeared in record 2007-07830-003.) The point estimate of sample coefficient alpha may provide a misleading impression of the reliability of the test score. Because sample coefficient alpha is consistently biased downward, it is more likely to yield a misleading impression of poor reliability. The magnitude of the bias is greatest precisely when the variability of sample alpha is greatest (small population reliability and small sample size). Taking into account the variability of sample alpha with an interval estimator may lead to retaining reliable tests that would be otherwise rejected. Here, the authors performed simulation studies to investigate the behavior of asymptotically distribution-free (ADF) versus normal-theory interval estimators of coefficient alpha under varied conditions. Normal-theory intervals were found to be less accurate when item skewness >1 or excess kurtosis >1. For sample sizes over 100 observations, ADF intervals are preferable, regardless of item skewness and kurtosis. A formula for computing ADF confidence intervals for coefficient alpha for tests of any size is provided, along with its implementation as an SAS macro. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Bootstrapping diagnoses using Bayes's theorem: It's not worth the trouble.

Notes that many DSM-III diagnostic procedures are based partly on the cutting of a symptom count at some predetermined point. S. E. Finn (see record 1982-30494-001) argued that base rates (prevalences) need to be used to modify the number of symptoms required for making a diagnosis. The present author considered 3 ways to estimate prevalence and diagnostic accuracy: (1) the reliability sample is gathered at random in the clinic, and the proportion of cases called ill by the criteria rater estimates the prevalence. (2) The reliability sample is used to estimate diagnostic accuracy, but the prevalence estimate is taken from a much larger sample. (3) The reliability sample is stratified by diagnosis, with 50% of the sample carrying the chart diagnosis of interest. Based on the assumption that 8 independent and equally valid signs count toward a diagnosis and that (at a cutting score of 5) the sensitivity and specificity of the fixed rule assume certain values, a computer program was written to perform bootstrap simulations. Results show that the improvements in diagnostic accuracy of such flexible diagnostic rules over DSM-III fixed symptom-count cutting scores were too small to justify their use. (7 ref) (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Estimation of sampling error variance in the meta-analysis of correlations: Use of average correlation in the homogeneous case.

The estimate of the population correlation used in the formula for sampling error variance of a correlation is typically the observed correlation, but in meta-analysis the average of the observed correlations can be used. For the case in which there is no variation in the study population correlations or sample sizes and the number of studies is very large, the authors found that use of the average correlation estimator is more accurate than use of the traditional, individual correlation estimator, except in those rare cases in which the uncorrected population correlation is greater than .60. For typical sample sizes, when the uncorrected population correlation is between -.40 and .40, there is virtually no error in the meta-analysis credibility interval based on the average correlation estimator. On the other hand, the amount of the error in the individual correlation estimator is qualitatively important if the sample is 25 or less and the population correlation is less than .40. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Decision rules for selecting effect sizes in meta-analysis: A review and reanalysis of psychotherapy outcome studies.

This study deals with some of the judgmental factors involved in selecting effect sizes from within the studies that enter a meta-analysis. Particular attention is paid to the conceptual redundancy rule that Smith, Glass, and Miller (1980) used in their study of the effectiveness of psychotherapy for deciding which effect sizes should and should not be counted in determining an overall effect size. Data from a random sample of 25 studies from Smith et al.'s (1980) population of psychotherapy outcome studies were first recoded and then reanalyzed meta-analytically. Using the conceptual redundancy rule, three coders independently coded effect sizes and identified more than twice as many of them per study as did Smith et al. Moreover, the treatment effect estimates associated with this larger sample of effects ranged between .30 and .50, about half the size claimed by Smith et al. Analyses of other rules for selecting effect sizes showed that average effect estimates also varied with these rules. Such results indicate that the average effect estimates derived from meta-analyses may depend heavily on judgmental factors that enter into how effect sizes are selected within each of the individual studies considered relevant to a meta-analysis. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

"Validity generalization and hypothetical reliability distributions: A test of the Schmidt-Hunter Procedure": Correction.

Reports an error in the original article by P. W. Paese and F. S. Switzer (Journal of Applied Psychology, 1988[May], Vol 73[2], 267–274). Observed artifactual variance (ARV) estimates were traced to an error in the Monte Carlo computer program. Results of the replication indicated that ARV was overestimated by the noninteractive equation. The interactive equation provided unbiased estimates of ARV. (The following abstract of this article originally appeared in record 1988-25308-001.) A Monte Carlo study was conducted to determine how variations in true reliability distributions affect validity generalization estimates that are based on hypothetical reliability distributions proposed by Schmidt and Hunter. Both interactive and noninteractive validity generalization equations were examined. True reliability distributions and sample sizes were systematically varied. Depending on the sample size and nature of the true distributions, ARV was either overestimated or underestimated by both equations. In some cases, extremely large errors were observed. Even when the data were generated with true reliability distributions identical to the hypothetical distributions, both equations systematically overestimated ARV… (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

On the sampling variance of intraclass correlations and genetic correlations

Widely used standard expressions for the sampling variance of intraclass correlations and genetic correlation coefficients were reviewed for small and large sample sizes. For the sampling variance of the intraclass correlation, it was shown by simulation that the commonly used expression, derived using a first-order Taylor series performs better than alternative expressions found in the literature, when the between-sire degrees of freedom were small. The expressions for the sampling variance of the genetic correlation are significantly biased for small sample sizes, in particular when the population values, or their estimates, are close to zero. It was shown, both analytically and by simulation, that this is because the estimate of the sampling variance becomes very large in these cases due to very small values of the denominator of the expressions. It was concluded, therefore, that for small samples, estimates of the heritabilities and genetic correlations should not be used in the expressions for the sampling variance of the genetic correlation. It was shown analytically that in cases where the population values of the heritabilities are known, using the estimated heritabilities rather than their true values to estimate the genetic correlation results in a lower sampling variance for the genetic correlation. Therefore, for large samples, estimates of heritabilities, and not their true values, should be used.     

Alterations in cyclin-dependent kinase 2 function during differentiation of primary human keratinocytes

Long-term care for the elderly has recently become an area of great interest for practicing social workers because of the increasing number of aged persons and the important role of government in financing and regulating their care. Therefore, the purpose of this study was to provide a set of estimates on patterns in long-term care service use among older Americans over an eight-year period. This study applied multinomial logistic regression to analyzing the data from the National Long-Term Care Survey of 1982-1989 (NLTCS). The results of this study showed a number of differences from the results with cross-sectional studies. Of the 6,393 sample persons, more than half (56.5%) died over the eight years from 1982 to 1989. The rate of entering nursing homes (12.6%) was low. The rate of using community-based care services was fairly low. About 10.4 percent of the sample received care from helping professional personnel or paid helpers. As expected, the number receiving care from kin and other informal support was high. Long-term care services in the United States were distributed very unequally among various social groups. The indicator of need was not the only determinant of service utilization. Other variables such as number of household members, race, age and education were also important for service utilization. The predictors of deceased versus informal help were need, age, number of household member, gender and marital status. The predictors of nursing home care versus informal help were need, age, number of household members, education, attitude toward nursing home and race. The predictors of community-based help care versus informal help were need, number of household members, and education.     

Relation to sample size to the stability of component patterns.

A variety of rules have been suggested for determining the sample size required to produce a stable solution when performing a factor or component analysis. The most popular rules suggest that sample size be determined as a function of the number of variables. These rules, however, lack both empirical support and a theoretical rationale. We used a Monte Carlo procedure to systematically vary sample size, number of variables, number of components, and component saturation (i.e., the magnitude of the correlation between the observed variables and the components) in order to examine the conditions under which a sample component pattern becomes stable relative to the population pattern. We compared patterns by means of a single summary statistic, g–2, and by means of direct pattern comparisons using the kappa statistic. Results indicated that, contrary to the popular rules, samples size as a function of the number of variables was not an important factor in determining stability. Component saturation and absolute sample size were the most important factors. To a lesser degree, the number of variables per component was also important, with variables per component producing more stable results. (PsycINFO Database Record (c) 2010 APA, all rights reserved)