Nick Martin and the 'Boulder Workshops'.

The author provides a personal perspective on Nick Martin's contributions to behavioral genetics and his role in the workshops on statistical genetics held annually in Boulder. Highlighted are Prof. Martin's seminal work on multivariate behavioral genetics, his career-long commitment to the value of the study of twins, and his enthusiastic support of the didactic mission of the 'Boulder workshops'. These contributions and activities continue unabated as we celebrate Prof. Martin's 70th birthday.

Statistical Power and the Classical Twin Design.

Dr Nick Martin has made enormous contributions to the field of behavior genetics over the past 50 years. Of his many seminal papers that have had a profound impact, we focus on his early work on the power of twin studies. He was among the first to recognize the importance of sample size calculation before conducting a study to ensure sufficient power to detect the effects of interest. The elegant approach he developed, based on the noncentral chi-squared distribution, has been adopted by subsequent researchers for other genetic study designs, and today remains a standard tool for power calculations in structural equation modeling and other areas of statistical analysis. The present brief article discusses the main aspects of his seminal paper, and how it led to subsequent developments, by him and others, as the field of behavior genetics evolved into the present era.

Type I Error Rates and Parameter Bias in Multivariate Behavioral Genetic Models.

For many multivariate twin models, the numerical Type I error rates are lower than theoretically expected rates using a likelihood ratio test (LRT), which implies that the significance threshold for statistical hypothesis tests is more conservative than most twin researchers realize. This makes the numerical Type II error rates higher than theoretically expected. Furthermore, the discrepancy between the observed and expected error rates increases as more variables are included in the analysis and can have profound implications for hypothesis testing and statistical inference. In two simulation studies, we examine the Type I error rates for the Cholesky decomposition and Correlated Factors models. Both show markedly lower than nominal Type I error rates under the null hypothesis, a discrepancy that increases with the number of variables in the model. In addition, we observe slightly biased parameter estimates for the Cholesky decomposition and Correlated Factors models. By contrast, if the variance-covariance matrices for variance components are estimated directly (without constraints), the numerical Type I error rates are consistent with theoretical expectations and there is no bias in the parameter estimates regardless of the number of variables analyzed. We call this the direct symmetric approach. It appears that each model-implied boundary, whether explicit or implicit, increases the discrepancy between the numerical and theoretical Type I error rates by truncating the sampling distributions of the variance components and inducing bias in the parameters. The direct symmetric approach has several advantages over other multivariate twin models as it corrects the Type I error rate and parameter bias issues, is easy to implement in current software, and has fewer optimization problems. Implications for past and future research, and potential limitations associated with direct estimation of genetic and environmental covariance matrices are discussed.

Memes and suicide.

The concept of memes is analyzed, and its applicability to suicidology explored. Proposals are made for possible memes implicated in suicidal behavior. A classification of suicidal memes is proposed and the relationship between memes and archetypes of suicide is discussed. It is suggested that the terminology of meme theory can sharpen research into imitation effects in suicide.

Association of cognitive distortions with problem and pathological gambling in adult male twins.

Treatment studies suggest that gambling-related irrational beliefs and attitudes (i.e., cognitive distortions (CDs)) contribute to the risk for problem gambling behavior. In a community sample of men, we investigated the associations among lifetime gambling-related CDs, psychiatric disorders other than pathological gambling , and problem gambling severity. Subjects were 1354 members of the Vietnam Era Twin Registry. Problem gambling and gambling-related CDs were derived from a 2002 interview using the National Opinion Research Center DSM-IV Screen for Gambling Problems (NODS). Exploratory factor analysis was performed with the 12 CD items to identify an underlying construct. Generalized linear models were computed to test for associations among CDs, psychiatric disorders other than pathological gambling, and gambling problem severity. Co-twin control analyses of monozygotic twin pairs discordant for problem gambling severity adjusted for genetic and shared environmental influences. Twelve CD items related to one underlying CD construct. After adjustment for lifetime psychiatric disorders, pathological gambling symptoms were positively associated with higher CD scores. Pathological gambling symptoms remained significantly associated with CD scores after controlling for genetic and shared environmental influence. These results provide empirical support for an association between gambling-related CDs and gambling problem severity, even after controlling for genetic and shared environmental influences and non-pathological gambling psychiatric disorders. Public health messages and therapeutic interventions that reinforce the randomness of gambling and draw attention to distorted thinking may prevent the development of problem gambling and improve treatment outcomes.

Design and implementation of a twin-family database for behavior genetics and genomics studies.

In this article we describe the design and implementation of a database for extended twin families. The database does not focus on probands or on index twins, as this approach becomes problematic when larger multigenerational families are included, when more than one set of multiples is present within a family, or when families turn out to be part of a larger pedigree. Instead, we present an alternative approach that uses a highly flexible notion of persons and relations. The relations among the subjects in the database have a one-to-many structure, are user-definable and extendible and support arbitrarily complicated pedigrees. Some additional characteristics of the database are highlighted, such as the storage of historical data, predefined expressions for advanced queries, output facilities for individuals and relations among individuals and an easy-to-use multi-step wizard for contacting participants. This solution presents a flexible approach to accommodate pedigrees of arbitrary size, multiple biological and nonbiological relationships among participants and dynamic changes in these relations that occur over time, which can be implemented for any type of multigenerational family study.

A Bayesian nonparametric meta-analysis model.

In a meta-analysis, it is important to specify a model that adequately describes the effect-size distribution of the underlying population of studies. The conventional normal fixed-effect and normal random-effects models assume a normal effect-size population distribution, conditionally on parameters and covariates. For estimating the mean overall effect size, such models may be adequate, but for prediction, they surely are not if the effect-size distribution exhibits non-normal behavior. To address this issue, we propose a Bayesian nonparametric meta-analysis model, which can describe a wider range of effect-size distributions, including unimodal symmetric distributions, as well as skewed and more multimodal distributions. We demonstrate our model through the analysis of real meta-analytic data arising from behavioral-genetic research. We compare the predictive performance of the Bayesian nonparametric model against various conventional and more modern normal fixed-effects and random-effects models.

A multivariate genetic analysis of the use of tobacco, alcohol, and caffeine in a population based sample of male and female twins.

Numerous epidemiologic studies in the past few decades have consistently demonstrated positive associations between the use of various psychoactive substances, both licit and illicit. This association could be due to shared genetic and/or shared environmental risk factors. This study uses multivariate structural equation modeling to determine the sources of covariation between the use of tobacco, alcohol, and caffeine, the three most commonly consumed psychoactive substances. In particular, we wish to clarify the extent to which genetic and environmental risk factors are shared across these three substances versus are substance specific in their effect. The sample, consisting of data collected from members of the population-based Virginia Twin Registry, consists of 774 monozygotic and 809 dizygotic male and female twin pairs. Our results demonstrate that genetic and individual specific environmental factors that are shared between these three substances account for a modest proportion of the total variance. For example, shared genetic risk factors across the three substances in males and females account for between 7 and 28% of the total variance in liability and 12-56% of the genetic variance. Common familial environment appears to play little or no role. Underlying genetic and individual environmental risk factors produce liability to (poly)substance use in general; substance specific factors also play an important etiologic role.

Social science methods for twins data: integrating causality, endowments, and heritability.

Twins have been extensively used in economics, sociology, and behavioral genetics to investigate the role of genetic endowments on a broad range of social, demographic, and economic outcomes. However, the focus in these literatures has been distinct.: The economic literature has been primarily concerned with the need to control for unobserved endowments--including as an important subset, genetic endowments--in analyses that attempt to establish the impact of one variable, often schooling, on a variety of economic, demographic, and health outcomes. Behavioral genetic analyses have mostly been concerned with decomposing the variation in the outcomes of interest into genetic, shared environmental, and non-shared environmental components, with recent multivariate analyses investigating the contributions of genes and the environment to the correlation and causation between variables. Despite the fact that twins studies and the recognition of the role of endowments are central to both of these literatures, they have mostly evolved independently. In this paper we develop formally the relationship between the economic and behavioral genetic approaches to the analyses of twins, and we develop an integrative approach that combines the identification of causal effects, which dominates the economic literature, with the decomposition of variances and covariances into genetic and environmental factors that are the primary goal of behavioral genetic approaches. We apply this integrative ACE-beta approach to an illustrative investigation of the impact of schooling on several demographic outcomes such as fertility and nuptiality and health.

A cautionary note on the use of simulation procedures for analyzing contingency tables containing small expected cell frequencies.

A comparison of a simple simulation procedure and exact tests for tables used in psychiatric genetic studies is performed, with focus on tables with small expected cell counts. The study shows that naive simulation procedures using uniform random numbers, could lead to conservative results, as compared with Fisher exact test for contingency tables, thus discarding as non-significant tables that are significant according to the exact test. Exact tests are recommended as an alternative to naive simulation for evaluating the statistical significance of contingency tables with small expected cell counts.

Likelihood ratio tests in behavioral genetics: problems and solutions.

The likelihood ratio test of nested models for family data plays an important role in the assessment of genetic and environmental influences on the variation in traits. The test is routinely based on the assumption that the test statistic follows a chi-square distribution under the null, with the number of restricted parameters as degrees of freedom. However, tests of variance components constrained to be non-negative correspond to tests of parameters on the boundary of the parameter space. In this situation the standard test procedure provides too large p-values and the use of the Akaike Information Criterion (AIC) or the Bayesian Information Criterion (BIC) for model selection is problematic. Focusing on the classical ACE twin model for univariate traits, we adapt existing theory to show that the asymptotic distribution for the likelihood ratio statistic is a mixture of chi-square distributions, and we derive the mixing probabilities. We conclude that when testing the AE or the CE model against the ACE model, the p-values obtained from using the chi(2)(1 df) as the reference distribution should be halved. When the E model is tested against the ACE model, a mixture of chi(2)(0 df), chi(2)(1 df) and chi(2)(2 df) should be used as the reference distribution, and we provide a simple formula to compute the mixing probabilities. Similar results for tests of the AE, DE and E models against the ADE model are also derived. Failing to use the appropriate reference distribution can lead to invalid conclusions.

Reinterpreting comorbidity: a model-based approach to understanding and classifying psychopathology.

Comorbidity has presented a persistent puzzle for psychopathology research. We review recent literature indicating that the puzzle of comorbidity is being solved by research fitting explicit quantitative models to data on comorbidity. We present a meta-analysis of a liability spectrum model of comorbidity, in which specific mental disorders are understood as manifestations of latent liability factors that explain comorbidity by virtue of their impact on multiple disorders. Nosological, structural, etiological, and psychological aspects of this liability spectrum approach to understanding comorbidity are discussed.

Cholesky problems.

Behavioral geneticists commonly parameterize a genetic or environmental covariance matrix as the product of a lower diagonal matrix postmultiplied by its transpose-a technique commonly referred to as "fitting a Cholesky." Here, simulations demonstrate that this procedure is sometimes valid, but at other times: (1) may not produce fit statistics that are distributed as a chi2; or (2) if the distribution of the fit statistic is chi2, then the degrees of freedom (df) are not always the difference between the number of parameters in the general model less the number of parameters in a constrained model. It is hypothesized that the problem is related to the fact that the Cholesky parameterization requires that the covariance matrix formed by the product be either positive definite or singular. Even though a population covariance matrix may be positive definite, the combination of sampling error and the derived--as opposed to directly observed--nature of genetic and environmental matrices allow matrices that are negative (semi) definite. When this occurs, fitting a Cholesky constrains the numerical area of search and compromises the maximum likelihood theory currently used in behavioral genetics. Until the reasons for this phenomenon are understood and satisfactory solutions are developed, those who fit Cholesky matrices face the burden of demonstrating the validity of their fit statistics and the df for model comparisons. An interim remedy is proposed--fit an unconstrained model and a Cholesky model, and if the two differ, then report the difference in fit statistics and parameter estimates. Cholesky problems are a matter of degree, not of kind. Thus, some Cholesky solutions will differ trivially from the unconstrained solutions, and the importance of the problems must be assessed by how often the two lead to different substantive interpretation of the results. If followed, the proposed interim remedy will develop a body of empirical data to assess the extent to which Cholesky problems are important substantive issues versus statistical curiosities.

Further considerations for power in sibling interaction models.

Sibling interactions aim to determine whether siblings' phenotype have an impact on one another. We explore the power to detect sibling interaction term in twin models with the inclusion of singletons (only children). Furthermore, we develop the existing work on the improvement of power from the addition of unrelateds (adoptive or step-siblings). We find that singletons are considerably more powerful under cooperative (positive or imitation) than competitive (negative) interaction. Additionally, the power from URs is attenuated when common environment is part of the genetic model.

Genotype-environment interactions in mouse behavior: a way out of the problem.

In behavior genetics, behavioral patterns of mouse genotypes, such as inbred strains, crosses, and knockouts, are characterized and compared to associate them with particular gene loci. Such genotype differences, however, are usually established in single-laboratory experiments, and questions have been raised regarding the replicability of the results in other laboratories. A recent multilaboratory experiment found significant laboratory effects and genotype x laboratory interactions even after rigorous standardization, raising the concern that results are idiosyncratic to a particular laboratory. This finding may be regarded by some critics as a serious shortcoming in behavior genetics. A different strategy is offered here: (i) recognize that even after investing much effort in identifying and eliminating causes for laboratory differences, genotype x laboratory interaction is an unavoidable fact of life. (ii) Incorporate this understanding into the statistical analysis of multilaboratory experiments using the mixed model. Such a statistical approach sets a higher benchmark for finding significant genotype differences. (iii) Develop behavioral assays and endpoints that are able to discriminate genetic differences even over the background of the interaction. (iv) Use the publicly available multilaboratory results in single-laboratory experiments. We use software-based strategy for exploring exploration (see) to analyze the open-field behavior in eight genotypes across three laboratories. Our results demonstrate that replicable behavioral measures can be practically established. Even though we address the replicability problem in behavioral genetics, our strategy is also applicable in other areas where concern about replicability has been raised.

The intraclass covariance matrix.

Introduced by C.R. Rao in 1945, the intraclass covariance matrix has seen little use in behavioral genetic research, despite the fact that it was developed to deal with family data. Here, I reintroduce this matrix, and outline its estimation and basic properties for data sets on pairs of relatives. The intraclass covariance matrix is appropriate whenever the research design or mathematical model treats the ordering of the members of a pair as random. Because the matrix has only one estimate of a population variance and covariance, both the observed matrix and the residual matrix from a fitted model are easy to inspect visually; there is no need to mentally average homologous statistics. Fitting a model to the intraclass matrix also gives the same log likelihood, likelihood-ratio (LR) chi2, and parameter estimates as fitting that model to the raw data. A major advantage of the intraclass matrix is that only two factors influence the LR chi2--the sampling error in estimating population parameters and the discrepancy between the model and the observed statistics. The more frequently used interclass covariance matrix adds a third factor to the chi2--sampling error of homologous statistics. Because of this, the degrees of freedom for fitting models to an intraclass matrix differ from fitting that model to an interclass matrix. Future research is needed to establish differences in power-if any--between the interclass and the intraclass matrix.

Exploratory factor analysis in behavior genetics research: factor recovery with small sample sizes.

Results of a Monte Carlo study of exploratory factor analysis demonstrate that in studies characterized by low sample sizes the population factor structure can be adequately recovered if communalities are high, model error is low, and few factors are retained. These are conditions likely to be encountered in behavior genetics research involving mean scores obtained from sets of inbred strains. Such studies are often characterized by a large number of measured variables relative to the number of strains used, highly reliable data, and high levels of communality. This combination of characteristics has special consequences for conducting factor analysis and interpreting results. Given that limitations on sample size are often unavoidable, it is recommended that researchers limit the number of expected factors as much as possible.

Sources of structure: genetic, environmental, and artifactual influences on the covariation of personality traits.

The phenotypic structure of personality traits has been well described, but it has not yet been explained causally. Behavior genetic covariance analyses can identify the underlying causes of phenotypic structure; previous behavior genetic research has suggested that the effects from both genetic and nonshared environmental influences mirror the phenotype. However, nonshared environmental effects are usually estimated as a residualterm that may also include systematic bias, such as that introduced by implicit personality theory. To reduce that bias, we supplemented data from Canadian and German twin studies with cross-observer correlations on the Revised NEO Personality Inventory. The hypothesized five-factor structure was found in both the phenotypic and genetic/familial covariances. When the residual covariance was decomposed into true nonshared environmental influences and method bias, only the latter showed the five-factor structure. True nonshared environmental influences are not structured as genetic influences are, although there was some suggestion that they do affect two personality dimensions, Conscientiousness and Love. These data reaffirm the value of behavior genetic analyses for research on the underlying causes of personality traits.

The heritability of alcohol abuse and dependence: a meta-analysis of behavior genetic research.

A meta-analysis was performed on 50 family, twin, and adoption studies in which problem drinking and alcohol dependence served as the primary criterion measure. The results showed that far from being an established "fact," the genetic foundations of alcohol misuse are modest and heterogeneous. A weighted mean phi effect size of 0.12 (95% Confidence Interval = 0.11-0.12) was obtained for the total sample of 72 effect sizes. Four potential moderator variables (proband gender, sample nationality, pattern severity, year of publication) were examined with outcomes confirming that the heritability of alcohol misuse is stronger in males and in studies employing more severe definitions of abuse (alcoholism, alcohol dependence). When the effect size measure was restricted to studies using male subjects with more severe diagnoses of alcohol misuse, the unweighted mean phi effect size was only 0.18 (95% Confidence Interval = 0.15-0.21), with an even smaller weighted mean phi effect size of 0.15 (95% Confidence Interval = 0.12-0.18); results which indicate an upper limit of 30-36% for the heritability of alcohol misuse.

The mixed or multilevel model for behavior genetic analysis.

We propose the mixed model or multilevel model as a general alternative approach to existing behavior genetic analysis-an alternative to correlation analysis, the DeFries-Fulker analysis, and structural equation modeling. The mixed or multilevel model handles readily families of behavioral genetic data, which include paired sibling data (e.g., pairs of MZ and DZ twins) and clustered sibling data (e.g., a family of more than two biological siblings) as special cases. Not only can a family of behavioral genetic data have more than two siblings, it can also contain multiple types of siblings (e.g., a pair of MZ twins, a pair of DZ twins, a full sibling, and a half sibling). In contrast to the traditional approaches, the mixed or multilevel model is insensitive to the order of the siblings in a sibling cluster. We apply our approach to a large, nationally representative behavior genetic sample collected recently by the Add Health Study. We demonstrate the approach through several applications using both clustered and family complex behavioral genetic data: conventional variance decomposition analysis, analysis of interactions between genetic and environmental influences, and analysis of the possible genetic basis for friendship selection. We compare results from the mixed or multilevel model, Pearson's correlation analysis, and the structural equation model.