A Maximum Entropy Procedure to Solve Likelihood Equations

In this article, we provide initial findings regarding the problem of solving likelihood equations by means of a maximum entropy (ME) approach. Unlike standard procedures that require equating the score function of the maximum likelihood problem at zero, we propose an alternative strategy where the score is instead used as an external informative constraint to the maximization of the convex Shannon\u2019s entropy function. The problem involves the reparameterization of the score parameters as expected values of discrete probability distributions where probabilities need to be estimated. This leads to a simpler situation where parameters are searched in smaller (hyper) simplex space. We assessed our proposal by means of empirical case studies and a simulation study, the latter involving the most critical case of logistic regression under data separation. The results suggested that the maximum entropy reformulation of the score problem solves the likelihood equation problem. Similarly, when maximum likelihood estimation is difficult, as is the case of logistic regression under separation, the maximum entropy proposal achieved results (numerically) comparable to those obtained by the Firth\u2019s bias-corrected approach. Overall, these first findings reveal that a maximum entropy solution can be considered as an alternative technique to solve the likelihood equation

Measuring insecure attachment in middle childhood: Psychometric evaluation of the short form of the Preoccupied and Avoidant Coping Questionnaire

The short form of the Preoccupied and Avoidant Coping Questionnaire (PACQ; Younger, Corby, Perry, 2005)is a widely used self-report questionnaire measuring insecure attachment toward mother and father in middle childhood. However, its factorial structure has not yet been examined, and evidence concerning its concurrent and convergent validity is extremely sparse. In Study 1 (N = 378, M = 9.37 years), we evaluated the factorial structure of the PACQ and its measurement invariance across Italian boys and girls. In Study 2 (N = 199, M = 9.27 years), we tested the mutual associations between the PACQ and the Experiences in Close Relationships\u2013Revised Child version (ECR-RC; Brenning, Van Petegem, Soenens, 2014), and their convergent and predictive validity. Results supported the factorial validity of the PACQ, its satisfactory internal consistency and structural invariance across child gender. However, findings lent only partial support to the association between the PACQ and the ECR-RC, and convergent and predictive validity were found only for the avoidance subscale of these questionnaires. Overall, the Italian version of the PACQ is a psychometrically sound instrument to assess insecure attachment in middle childhood, but further research is needed to shed light on the conceptual significance of the preoccupied dimension

Using Harter and Likert Response Formats in Middle Childhood: A Comparison of Attachment Measures

Self-report questionnaires based on Harter's response format ("Some kids . . . but other kids . . . ") are commonly used in developmental and clinical research settings, but the reliability and validity of this format in middle childhood are still under debate. The current study aimed to test the psychometric proprieties of Harter versus Likert response formats as applied to two attachment questionnaires in a sample of 410 Italian children aged 8 to 10 years. Participants completed the Experiences in Close Relationships-Revised Child version ( n = 102, 4-point Likert-type scale; n = 104, adapted Harter version) and the Security Scale ( n = 95, Harter's format; n = 109 adapted 4-point Likert version). Results of multigroup confirmatory factor analyses indicated that the two response formats exhibited comparable reliability and factorial validity, although a slight superiority of Harter's format emerged for the Security Scale. External validity was supported for both answer formats. Implications for developmental theory and practice are discussed

Effect of the symbolic meaning of speed on the perceived duration of children and adults

The present study investigated how the symbolic meaning of speed affects time perception in children and adults. We employed a time reproduction task in which participants were asked to reproduce temporal intervals previously presented. In Experiment 1, 45 primary school children and 22 university students performed a time reproduction task with cars (meaning of fastness) and trucks (meaning of slowness) presented for 11 and 21 s in static and moving conditions. Results showed that young children under-reproduced the duration more than the older children and adults, especially when the stimulus presented was a car. Moreover, participants under-reproduced moving stimuli compared to static one. In Experiment 2, we tested 289 participants who were divided into nine different age groups according to their school class: five from primary school, three from Junior High, and one from the university. Participants performed a time reproduction task with a motorbike (meaning of fastness) or a bicycle (meaning of slowness) under static and moving conditions for 11, 21, and 36 s. The results confirmed the effects of symbolic meaning of speed on children\u2019s time perception and showed that vehicles that evoked the idea of fastness were under-reproduced compared to stimuli evoking the idea of slowness