Distilling vector space model scores for the assessment of constructed responses with bifactor Inbuilt Rubric method and latent variables

Abstract

In this paper, we highlight the importance of distilling the computational assessments of constructed responses to validate the indicators/proxies of constructs/trins using an empirical illustration in automated summary evaluation. We present the validation of the Inbuilt Rubric (IR) method that maps rubrics into vector spaces for concepts’ assessment. Specifically, we improved and validated its scores’ performance using latent variables, a common approach in psychometrics. We also validated a new hierarchical vector space, namely a bifactor IR. 205 Spanish undergraduate students produced 615 summaries of three different texts that were evaluated by human raters and different versions of the IR method using latent semantic analysis (LSA). The computational scores were validated using multiple linear regressions and different latent variable models like CFAs or SEMs. Convergent and discriminant validity was found for the IR scores using human rater scores as validity criteria. While this study was conducted in the Spanish language, the proposed scheme is language-independent and applicable to any language. We highlight four main conclusions: (1) Accurate performance can be observed in topic-detection tasks without hundreds/thousands of pre-scored samples required in supervised models. (2) Convergent/discriminant validity can be improved using measurement models for computational scores as they adjust for measurement errors. (3) Nouns embedded in fragments of instructional text can be an affordable alternative to use the IR method. (4) Hierarchical models, like the bifactor IR, can increase the validity of computational assessments evaluating general and specific knowledge in vector space models. R code is provided to apply the classic and bifactor IR method.