{"title":"快速估计具有顺序、连续和计数观测变量的性能和过程数据的广义线性潜变量模型。","authors":"Maoxin Zhang, Björn Andersson, Shaobo Jin","doi":"10.1111/bmsp.12337","DOIUrl":null,"url":null,"abstract":"<p>Different data types often occur in psychological and educational measurement such as computer-based assessments that record performance and process data (e.g., response times and the number of actions). Modelling such data requires specific models for each data type and accommodating complex dependencies between multiple variables. Generalized linear latent variable models are suitable for modelling mixed data simultaneously, but estimation can be computationally demanding. A fast solution is to use Laplace approximations, but existing implementations of joint modelling of mixed data types are limited to ordinal and continuous data. To address this limitation, we derive an efficient estimation method that uses first- or second-order Laplace approximations to simultaneously model ordinal data, continuous data, and count data. We illustrate the approach with an example and conduct simulations to evaluate the performance of the method in terms of estimation efficiency, convergence, and parameter recovery. The results suggest that the second-order Laplace approximation achieves a higher convergence rate and produces accurate yet fast parameter estimates compared to the first-order Laplace approximation, while the time cost increases with higher model complexity. Additionally, models that consider the dependence of variables from the same stimulus fit the empirical data substantially better than models that disregarded the dependence.</p>","PeriodicalId":55322,"journal":{"name":"British Journal of Mathematical & Statistical Psychology","volume":"77 3","pages":"477-507"},"PeriodicalIF":1.5000,"publicationDate":"2024-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/bmsp.12337","citationCount":"0","resultStr":"{\"title\":\"Fast estimation of generalized linear latent variable models for performance and process data with ordinal, continuous, and count observed variables\",\"authors\":\"Maoxin Zhang, Björn Andersson, Shaobo Jin\",\"doi\":\"10.1111/bmsp.12337\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>Different data types often occur in psychological and educational measurement such as computer-based assessments that record performance and process data (e.g., response times and the number of actions). Modelling such data requires specific models for each data type and accommodating complex dependencies between multiple variables. Generalized linear latent variable models are suitable for modelling mixed data simultaneously, but estimation can be computationally demanding. A fast solution is to use Laplace approximations, but existing implementations of joint modelling of mixed data types are limited to ordinal and continuous data. To address this limitation, we derive an efficient estimation method that uses first- or second-order Laplace approximations to simultaneously model ordinal data, continuous data, and count data. We illustrate the approach with an example and conduct simulations to evaluate the performance of the method in terms of estimation efficiency, convergence, and parameter recovery. The results suggest that the second-order Laplace approximation achieves a higher convergence rate and produces accurate yet fast parameter estimates compared to the first-order Laplace approximation, while the time cost increases with higher model complexity. Additionally, models that consider the dependence of variables from the same stimulus fit the empirical data substantially better than models that disregarded the dependence.</p>\",\"PeriodicalId\":55322,\"journal\":{\"name\":\"British Journal of Mathematical & Statistical Psychology\",\"volume\":\"77 3\",\"pages\":\"477-507\"},\"PeriodicalIF\":1.5000,\"publicationDate\":\"2024-02-12\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://onlinelibrary.wiley.com/doi/epdf/10.1111/bmsp.12337\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"British Journal of Mathematical & Statistical Psychology\",\"FirstCategoryId\":\"102\",\"ListUrlMain\":\"https://onlinelibrary.wiley.com/doi/10.1111/bmsp.12337\",\"RegionNum\":3,\"RegionCategory\":\"心理学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS, INTERDISCIPLINARY APPLICATIONS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"British Journal of Mathematical & Statistical Psychology","FirstCategoryId":"102","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1111/bmsp.12337","RegionNum":3,"RegionCategory":"心理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS, INTERDISCIPLINARY APPLICATIONS","Score":null,"Total":0}
Fast estimation of generalized linear latent variable models for performance and process data with ordinal, continuous, and count observed variables
Different data types often occur in psychological and educational measurement such as computer-based assessments that record performance and process data (e.g., response times and the number of actions). Modelling such data requires specific models for each data type and accommodating complex dependencies between multiple variables. Generalized linear latent variable models are suitable for modelling mixed data simultaneously, but estimation can be computationally demanding. A fast solution is to use Laplace approximations, but existing implementations of joint modelling of mixed data types are limited to ordinal and continuous data. To address this limitation, we derive an efficient estimation method that uses first- or second-order Laplace approximations to simultaneously model ordinal data, continuous data, and count data. We illustrate the approach with an example and conduct simulations to evaluate the performance of the method in terms of estimation efficiency, convergence, and parameter recovery. The results suggest that the second-order Laplace approximation achieves a higher convergence rate and produces accurate yet fast parameter estimates compared to the first-order Laplace approximation, while the time cost increases with higher model complexity. Additionally, models that consider the dependence of variables from the same stimulus fit the empirical data substantially better than models that disregarded the dependence.
期刊介绍:
The British Journal of Mathematical and Statistical Psychology publishes articles relating to areas of psychology which have a greater mathematical or statistical aspect of their argument than is usually acceptable to other journals including:
• mathematical psychology
• statistics
• psychometrics
• decision making
• psychophysics
• classification
• relevant areas of mathematics, computing and computer software
These include articles that address substantitive psychological issues or that develop and extend techniques useful to psychologists. New models for psychological processes, new approaches to existing data, critiques of existing models and improved algorithms for estimating the parameters of a model are examples of articles which may be favoured.