Componentes de dificultad de tareas de razonamiento deductivo aplicando el modelo LLTM de Fischer / Difficulty components of deductive reasoning tasks by applying Fischer's LLTM model

El razonamiento silogístico es parte importante del razonamiento deductivo. El análisis de las fuentes de error en la resolución de silogismos originó, dentro de la psicología cognitiva, explicaciones como el efecto atmósfera, el sesgo de la figura y la conversión ilícita. En este trabajo se ajustó el modelo LLTM de Fischer para identificar componentes de dificultad de silogismos y estimar sus efectos. Se administraron 46 ítems con un diseño de enlace a tres grupos, con un total de 1074 estudiantes universitarios. Para cada par de premisas se debía escoger un esquema de conclusión y completarlo con los términos extremos o reconocer la falta de conclusión válida. El modelo de Rasch se ajustó sobre un subconjunto de 20 silogismos y se aplicó el modelo LLTM de Fischer. Se identificaron, aumentando la dificultad, cuatro componentes: efecto atmósfera y sesgo de figura (cuando éstos están en dirección contraria a la conclusión o no hay conclusión válida), figura II y figura III. El carácter reversible de la conclusión (modos universal negativo y particular afirmativo) y la falta de conclusión válida fueron componentes facilitadores. La correlación entre las estimaciones de los parámetros de dificultad bajo el modelo de Rasch y el LLTM fue 0,96.

Syllogistic reasoning is an important part of deductive reasoning. In cognitive psychology, the analysis of error sources in solving syllogisms produced explanations such as the atmosphere effect, figure bias and wrong conversion. The Fischer Linear Logistic Test Model (LLTM) was fitted on a set of syllogisms in order to identify their difficulty components and estimate their effects. Forty six items were administered with a link design to three groups of 1074 university students. The task consisted in choosing, for each pair of premises, one conclusion scheme and complete it with the suitable terms, if a valid conclusion existed; otherwise, examinees had to select the option of no valid conclusion. The Rasch model was fitted to a subset of 20 syllogisms on which Fischer's LLTM was applied. Four components were identified that increase syllogistic difficulty: atmosphere effect, figure bias (when they follow the opposite direction of the conclusion or when there is no valid conclusion), figure II and figure III. Two components were found that make the task easier: reversibility of conclusion (universal negative and particular affirmative modes) and lack of valid conclusion. Linear correlation between the estimates of difficulty parameters obtained with Rasch and LLTM models was .96.

Análisis de los componentes en la adquisición de la lectura en castellano: una aplicación del modelo logístico lineal / Component analysis of Spanish reading process: an application of the linear logistic test model

Se analizan los componentes básicos para la adquisición de la lectura en castellano mediante la aplicación del modelo logístico lineal de Fisher (Linear Logistic Test Model [LLTM]). Participaron en el estudio 245 niños y niñas de edades comprendidas entre los 4 y los 9 años a los que se administró una extensa batería diseñada para evaluar distintos procesos básicos para la lectura (PROBALES). Se aplicaron técnicas de análisis factorial para seleccionar un subconjunto de ítems que mostrasen ajuste al modelo de Rasch. El LLTM permitió confirmar la validez del modelo teórico según el cual el aprendizaje de la lectura descansa en el desarrollo de tres habilidades básicas: reconocimiento de palabras, conciencia fonológica y comprensión de la lectura. Se muestra la capacidad predictiva del modelo mediante análisis discriminante, y se constata que se clasificó correctamente en su curso escolar al 68% de los participantes.

The basic components for the acquisition of reading in Spanish are analyzed by using the Fisher Linear Logistic Test Model (LLTM). An extensive battery designed to assess different Basic Processes for Reading (PROBALES, acronym in Spanish) was applied to 245 children aged 4 to 9. Factor analysis techniques were used to select a subset of items that would adjust to the Rasch model. The LLTM confirmed the validity of the theoretical model which states that reading acquisition relies on the development of three basic skills: word recognition, phonological awareness, and reading comprehension. The theoretical model's predictive ability is shown by discriminant analysis, thereby confirming that 68% of participants were correctly classified in their school grade.

Aplicación del modelo LLTM de Fischer al análisis de las fuentes de dificultad de ítemes de razonamiento deductivo / Application of the Fischer LLTM model to the analysis of the sources of difficulty of deductive reasoning items

El Modelo Logístico Lineal de Rasgo Latente (LLTM) de Fischer permite descomponer la dificultad de un ítem como suma de los efectos debidos a las fuentes de dificultad predichas por las teorías cognitivas, decidir si éstos son significativos y estimarlos. En el estudio que se informa se diseñaron y elaboraron 24 ítemes de razonamiento deductivo teniendo en cuenta las fuentes de dificultad predichas por las teorías cognitivas y por la experiencia educacional. Se administraron a 251 estudiantes de la Carrera de Psicología de la Universidad de Buenos Aires (UBA). Se describe el procedimiento para seleccionar un subconjunto de los mismos al cual ajuste el modelo LLTM. El objetivo de este trabajo fue verificar la pertinencia de las fuentes de dificultad consideradas y orientar la construcción de nuevos ítemes. Se logró un buen ajuste del modelo de Rasch (p = .89) y del modelo LLTM (p = .11) sobre 12 de ellos. Los valores z de Wald resultaron no significativos para los 12 ítemes mencionados. La correlación de los parámetros de dificultad estimados en ambos modelos fue: r = .99. Se consideraron cinco componentes que resultaron significativos. Éstos fueron, en orden decreciente de dificultad, la presencia de: (a) falacias de afirmación del consecuente y de negación del antecedente, (b) negación afectando a la disyunción o conjunción, (c) contenido abstracto o simbólico, (d) cuantificadores y (e) condicionales. Se verificaron los supuestos de invariancia para los parámetros de los ítemes y de los sujetos. Los resultados de esta etapa exploratoria alientan a seguir construyendo ítemes tomando en cuenta las fuentes de dificultad halladas.

The processes involved in deductive reasoning have been studied by Cognitive Psychology since the seventies. Many hypotheses have been put forward to explain the difficulties in solving simple reasoning problems when considering their logical connectives, content and context of the tasks in which they are presented. These hypotheses have led to the development of different theories of reasoning like those based on the formal inference rules approach (Braine, 1978; Braine & O'Brien, 1991; Braine & Rumain, 1983; Rips, 1994), the Pragmatic Schemas Theory (Cheng & Holyoak, 1985) and the theory of semantic mental models (Johnson-Laird, 1983, Johnson-Laird & Byrne, 1991). The componential models of the Item Response Theory have allowed Psychometry to explain said these processes (Embretson, 1994). Thus, for instance, the Linear Logistic Latent Trait Model (LLTM) (Fischer, 1973, 1997), an extension of the Rasch model, expresses item difficulty as the sum of the effects due to the sources of difficulty predicted by the mentioned cognitive theories, which enables us to decide whether these effects are significant and estimate them. In other words, the Rasch item parameters β1 are linearly decomposed in the form where p is the number of components considered, αl -the basic parameters of the model, expresses the difficulty of each component l, w il is the weight of αl with respect to the difficulty of the item i and c is an arbitrary normalization constant. Formula (1) implies that the application of the LLTM model makes sense only when the Rasch model fits the data. On the other hand, if the proposed components were sufficiently exhaustive to explain the differences between the items, formula (1) would allow us, once the basic parameters αl have been estimated, to recover estimates similar to those obtained directly by the application of the Rasch model, which would imply a high correlation between the parameters estimated under both models. The identification of the difficulty components and the estimate of their effects may be useful to generate items with preset difficulty parameters. This paper describes the process to find a subset of deductive reasoning items to which the LLTM model fits well. A set of 24 deductive reasoning items were designed and created considering the sources of difficulty predicted by cognitive theories and educational practice. The objective is to verify the suitability of such sources and to guide the construction of new items. Each item may consist of one, two or three premises and one conclusion. The individual must decide whether the conclusion is true or false. Nine items are made of concrete content, neutral to avoid any bias due beliefs or opinions, and the remaining ones have abstract or symbolic content. They were administered to a sample of 251 students of Psychology (Universidad de Buenos Aires - Argentina), composed of 24% males and 76% females, whose average age is 22.68 (DS = 6.35). Good fit for the Rasch model (p = .89) and for the LLTM model (p = .11) were obtained for 12 of them. The Wald z-values were not significant for the 12 items mentioned before. The linear correlation between the parameters estimated under both models was r = .99. Five components that turned out to be significant were considered. These components are listed in a decreasing level of difficulty: (a) affirmation of the consequent and negation of antecedent fallacies, (b) negation when affecting disjunction / conjunction, (c) abstract or symbolic content, (d) quantifiers and (e) conditionals. The two assumptions that refer to both, the item and subject parameter invariance, were checked. The results of this exploratory step encourage us to go on constructing new items taking into account the sources of difficulty that were found.