A Thurstonian model is a stochastic transitivity model with latent variables for describing the mapping of some continuous scale onto discrete, possibly ordered categories of response. In the model, each of these categories of response corresponds to a latent variable whose value is drawn from a normal distribution, independently of the other response variables and with constant variance. Developments over the last two decades, however, have led to Thurstonian models that allow unequal variance and non zero covariance terms. Thurstonian models have been used as an alternative to generalized linear models in analysis of sensory discrimination tasks. They have also been used to model long-term memory in ranking tasks of ordered alternatives, such as the order of the amendments to the US Cons
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| - Modelo thurstoniano (es)
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| - Un modelo thurstoniano es un modelo de transitividad estocástica con variables latentes para describir el mapeo de alguna escala continua en categorías de respuesta discretas, posiblemente ordenadas. En el modelo, cada una de estas categorías de respuesta corresponde a una variable latente cuyo valor se extrae de una distribución normal, independientemente de las demás variables de respuesta y con varianza constante. Sin embargo, los desarrollos en las últimas dos décadas han llevado a modelos thurstonianos que permiten una varianza desigual y términos de covarianza distintos de cero. Los modelos thurstonianos se han utilizado como una alternativa a los modelos lineales generalizados en el análisis de tareas de discriminación sensorial. También se han utilizado para modelar la memoria a l (es)
- A Thurstonian model is a stochastic transitivity model with latent variables for describing the mapping of some continuous scale onto discrete, possibly ordered categories of response. In the model, each of these categories of response corresponds to a latent variable whose value is drawn from a normal distribution, independently of the other response variables and with constant variance. Developments over the last two decades, however, have led to Thurstonian models that allow unequal variance and non zero covariance terms. Thurstonian models have been used as an alternative to generalized linear models in analysis of sensory discrimination tasks. They have also been used to model long-term memory in ranking tasks of ordered alternatives, such as the order of the amendments to the US Cons (en)
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| - Un modelo thurstoniano es un modelo de transitividad estocástica con variables latentes para describir el mapeo de alguna escala continua en categorías de respuesta discretas, posiblemente ordenadas. En el modelo, cada una de estas categorías de respuesta corresponde a una variable latente cuyo valor se extrae de una distribución normal, independientemente de las demás variables de respuesta y con varianza constante. Sin embargo, los desarrollos en las últimas dos décadas han llevado a modelos thurstonianos que permiten una varianza desigual y términos de covarianza distintos de cero. Los modelos thurstonianos se han utilizado como una alternativa a los modelos lineales generalizados en el análisis de tareas de discriminación sensorial. También se han utilizado para modelar la memoria a largo plazo en la clasificación de tareas de alternativas ordenadas, como el orden de las enmiendas a la Constitución de Estados Unidos. Su principal ventaja sobre otras tareas de clasificación de modelos es que dan cuenta de la no independencia de las alternativas. Ennis proporciona una descripción completa de la derivación de modelos thurstonianos para una amplia variedad de tareas de comportamiento, incluida la elección preferencial, calificaciones, tríadas, tétradas, par dual, igual-diferente y grado de diferencia, rangos, primera y última elección y puntuación de aplicabilidad. (es)
- A Thurstonian model is a stochastic transitivity model with latent variables for describing the mapping of some continuous scale onto discrete, possibly ordered categories of response. In the model, each of these categories of response corresponds to a latent variable whose value is drawn from a normal distribution, independently of the other response variables and with constant variance. Developments over the last two decades, however, have led to Thurstonian models that allow unequal variance and non zero covariance terms. Thurstonian models have been used as an alternative to generalized linear models in analysis of sensory discrimination tasks. They have also been used to model long-term memory in ranking tasks of ordered alternatives, such as the order of the amendments to the US Constitution. Their main advantage over other models ranking tasks is that they account for non-independence of alternatives. Ennis provides a comprehensive account of the derivation of Thurstonian models for a wide variety of behavioral tasks including preferential choice, ratings, triads, tetrads, dual pair, same-different and degree of difference, ranks, first-last choice, and applicability scoring. In Chapter 7 of this book, a closed form expression, derived in 1988, is given for a Euclidean-Gaussian similarity model that provides a solution to the well-known problem that many Thurstonian models are computationally complex often involving multiple integration. In Chapter 10, a simple form for ranking tasks is presented that only involves the product of univariate normal distribution functions and includes rank-induced dependency parameters. A theorem is proven that shows that the particular form of the dependency parameters provides the only way that this simplification is possible. Chapter 6 links discrimination, identification and preferential choice through a common multivariate model in the form of weighted sums of central F distribution functions and allows a general variance-covariance matrix for the items. (en)
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