Calculation of the Probability Distribution of CIBS Score in Different Relationships and Its Application / 法医学杂志

Objective To derive the probability distribution formula of combined identity by state （CIBS） score among individuals with different relationships based on population data of autosomal multiallelic genetic markers. Methods The probabilities of different identity by state （IBS） scores occurring at a single locus between two individuals with different relationships were derived based on the principle of ITO method. Then the distribution probability formula of CIBS score between two individuals with different relationships when a certain number of genetic markers were used for relationship identification was derived based on the multinomial distribution theory. The formula was compared with the CIBS probability distribution formula based on binomial distribution theory. Results Between individuals with a certain relationship, labelled as RS, the probabilities of IBS=2, 1 and 0 occurring at a certain autosomal genetic marker x （that is, p2（RSx）, p1（RSx） and p0（RSx））, can be calculated based on the allele frequency data of that genetic marker and the probability of two individuals with the corresponding RS relationship sharing 0, 1 or 2 identity by descent （IBD） alleles （that is, φ0, φ1 and φ2）. For a genotyping system with multiple independent genetic markers, the distribution of CIBS score between pairs of individuals with relationships other than parent-child can be deducted using the averages of the 3 probabilities of all genetic markers （that is, p2（RS）, p1（RS） and p0（RS））, based on multinomial distribution theory. Conclusion The calculation of CIBS score distribution formula can be extended to all kinships and has great application value in case interpretation and system effectiveness evaluation. In most situations, the results based on binomial distribution formula are similar to those based on the formula derived in this study, thus, there is little difference between the two methods in actual work.

Modelagem multinomial aplicada à pesquisa em psicologia / Modelo multinomial aplicado a la investigación psicológica / Multinomial modeling applied to psychological research

Teorias sobre fenômenos psicológicos frequentemente fazem referência a processos que não são diretamente observáveis (processos latentes). Tradicionalmente, no entanto, a investigação desses fenômenos é feita de forma indireta aos processos latentes. O objetivo deste artigo é introduzir os conceitos fundamentais de modelagem multinomial. Aqui mostramos como modelos de processos latentes são derivados de modelos puramente descritivos através da redução do espaço de parâmetros motivada por uma ou mais teorias psicológicas. Os resultados são os modelos multinomiais que fornecem medidas simples de processos psicológicos (probabilidades) e que podem ser quantitativamente testados com dados reais. O uso de modelagem multinomial permite a análise direta dos efeitos de variáveis independentes nos próprios processos latentes que controlam o desempenho em uma ou mais tarefas experimentais, assim, facilitando o teste de predições e explicações teóricas sobre fenômenos psicológicos.

Theories about psychological phenomena often refer to unobservable processes (latent processes). Traditionally, however, the psychological investigation of these phenomena is done indirectly to the latent processes themselves. The objective of this article is to introduce fundamental concepts about multinomial modeling. Here we show that latent processes models are derived from purely descriptive models by reducing the parameter space according to one or more psychological theories. The result is multinomial models that deliver simple measures of psychological processes (probabilities) and that can be tested quantitatively with real data. The use of multinomial modeling allows direct analysis of the effects of independent variables on the latent processes that control performance on one or more experimental tasks, thus making it easier to test theoretical predictions and explanations about psychological phenomena.

Teorías sobre fenómenos psicológicos a menudo se refieren a procesos que no son directamente observables (procesos latentes). Sin embargo, la investigación de estos fenómenos se realiza tradicionalmente de manera indirecta con respecto a los procesos latentes. El propósito de este artículo es presentar los conceptos fundamentales del modelado multinomial. Aquí mostramos cómo los modelos de procesos latentes se derivan de modelos puramente descriptivos al reducir el espacio de parámetros motivado por una o más teorías psicológicas. El resultado son modelos multinomiales que proporcionan medidas simples de procesos psicológicos (probabilidades) y que pueden probarse cuantitativamente con datos reales. El uso de modelos multinomiales permite el análisis directo de los efectos de variables independientes en los procesos latentes que controlan el rendimiento en una o más tareas experimentales, lo que facilita la prueba de predicciones y explicaciones teóricas sobre fenómenos psicológicos.

Comparing discrete distributions when the sample space is smal / Comparando las distribuciones discretas cuando el espacio muestral es pequeño

This paper describes two new methods for comparing two independent, discrete distributions, when the sample space is small, using an extension of the Storer-Kim method for comparing independent binomials. These methods are relevant, for example, when comparing groups based on a Likert scale, which was the motivation for the paper. In essence, the goal is to test the hypothesis that the cell probabilities associated with two independent multinomial distributions are equal. Both a global test and a multiple comparison procedure are proposed. The small-sample properties of both methods are compared to four other techniques via simulations: Cliff's generalization of the Wilcoxon-Mann-Whitney test that effectively deals with heteroscedasticity and tied values, Yuen's test based on trimmed means, Welch's test and Student's t test. For the simulations, data were generated from beta-binomial distributions. Both symmetric and skewed distributions were used. The sample space consisted of the integers 0(1)4 or 0(1)10. For the global test that is proposed, when testing at the 0.05 level, simulation estimates of the actual Type I error probability ranged between 0.043 and 0.059. For the new multiple comparison procedure, the estimated family wise error rate ranged between 0.031 and 0.054 for the sample space 0(1)4. But for 0(1)10, the estimates dropped as low as 0.016 in some situations. Given the goal of comparing means, Student's t is well known to have practical problems when distributions differ. Similar problems are found here among the situations considered. No single method dominates in terms of power, as would be expected, because different methods are sensitive to different features of the distributions being compared. But in general, one of the new methods tends to have relatively good power based on both simulations and experience with data from actual studies. If, however, there is explicit interest in comparing means, rather than comparing the cell probabilities, Welch's test was found to perform well. The new methods are illustrated using data from the Well-Elderly Study where the goal is to compare groups in terms of depression and the strategies used for dealing with stress.

En este artículo se describen dos nuevos métodos para comparar dos distribuciones discretas independientes, cuando el espacio muestral es pequeño, usando una extensión del método Storer-Kim para comparar binomios independientes. Estos métodos son relevantes, por ejemplo, cuando se comparan grupos basados en una escala Likert, la cual motivó la escritura del artículo. En esencia, el objetivo es evaluar la hipótesis de que las probabilidades de células asociadas con dos distribuciones multinominales independientes son iguales. Se propone una prueba global y un procedimiento de comparación múltiple. Las propiedades de las muestras pequeñas de ambos métodos fueron comparadas con otras cuatro técnicas a través de simulaciones: generalización de Cliff de la prueba de Wilcoxon-Mann-Whitney que trata eficazmente con heteroscedasticidad y valores vinculados, la prueba de Yuen basada en medias truncadas, la prueba de Welch y la prueba t de Student. Para las simulaciones, los datos se generaron a partir de distribuciones beta-binomiales. Se utilizaron distribuciones tanto simétricas como asimétricas. El espacio muestral consistió en los enteros 0(1)4 o 0(1)10. Para la prueba global que se propone, cuando se evaluó al nivel de 0.05, la simulación estimó la probabilidad del error tipo I osciló entre 0.043 y 0.059. Para el nuevo procedimiento de comparación múltiple, la tasa de error estimada oscilaba entre 0.031 y 0.054 para el espacio de la muestra 0(1)4. Pero para 0(1)10, las estimaciones fueron tan bajas como 0.016 en algunas situaciones. Teniendo en cuenta el objetivo de la comparación de medias, la prueba t de Student es bien conocida por tener problemas prácticos cuando distribuciones difieren. Problemas similares se encuentraron entre las situaciones consideradas. No existe un único método que domina en términos de poder, como sería de esperar, debido a que los diferentes métodos son sensibles a las diferentes características de las distribuciones que son comparadas. Pero en general, uno de los nuevos métodos tiende a tener relativamente buen poder basado tanto en simulaciones y la experiencia con los datos de estudios reales. Si, sin embargo, existe un interés explícito en comparar medias, en lugar de comparar las probabilidades de celda, la prueba de Welch se encuentra que tiene un buen desempeño. Los nuevos métodos se ilustran usando datos del estudio Well-Elderly donde el objetivo es comparar los grupos en cuanto a la depresión y las estrategias utilizadas para hacer frente al estrés.