Purpose – Factor analysis is the most used tool in organizational research and its widespread use in scale validations contribute to decision-making in management. However, standard factor analysis is not always applied correctly mainly due to the misuse of ordinal data as interval data and the inadequacy of the former for classical factor analysis. The purpose of this paper is to present and apply the Bayesian factor analysis for mixed data (BFAMD) in the context of empirical using the Bayesian paradigm for the construction of scales. Design/methodology/approach – Ignoring the categorical nature of some variables often used in management studies, as the popular Likert scale, may result in a model with false accuracy and possibly biased estimates. To address this issue, Quinn (2004) proposed a Bayesian factor analysis model for mixed data, which is capable of modeling ordinal (qualitative measure) and continuous data (quantitative measure) jointly and allows the inclusion of qualitative information through prior distributions for the parameters’ model. This model, adopted here, presents considering advantages and allows the estimation of the posterior distribution for the latent variables estimated, making the process of inference easier. Findings – The results show that BFAMD is an effective approach for scale validation in management studies making both exploratory and confirmatory analyses possible for the estimated factors and also allowing the analysts to insert a priori information regardless of the sample size, either by using the credible intervals for Factor Loadings or by conducting specific hypotheses tests. The flexibility of the Bayesian approach presented is counterbalanced by the fact that the main estimates used in factor analysis as uniqueness and communalities commonly lose their usual interpretation due to the choice of using prior distributions. Originality/value – Considering that the development of scales through factor analysis aims to contribute to appropriate decision-making in management and the increasing misuse of ordinal scales as interval in organizational studies, this proposal seems to be effective for mixed data analyses. The findings found here are not intended to be conclusive or limiting but offer a useful starting point from which further theoretical and empirical research of Bayesian factor analysis can be built.

中文翻译：

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管理研究混合数据的贝叶斯因子分析

目的——因子分析是组织研究中最常用的工具，它在规模验证中的广泛使用有助于管理决策。然而，标准因子分析并不总是正确应用，主要是由于将序数数据误用为区间数据，以及前者不适用于经典因子分析。本文的目的是在使用贝叶斯范式构建量表的经验背景下，介绍和应用混合数据的贝叶斯因子分析 (BFAMD)。设计/方法/方法——忽略管理研究中经常使用的一些变量的分类性质，因为流行的李克特量表可能会导致模型具有错误的准确性和可能有偏差的估计。为了解决这个问题，Quinn (2004) 提出了一种混合数据的贝叶斯因子分析模型，它能够联合建模序数（定性度量）和连续数据（定量度量），并允许通过参数模型的先验分布包含定性信息。此处采用的该模型具有考虑优势，并允许估计潜在变量的后验分布，从而使推理过程更容易。结果——结果表明，BFAMD 是管理研究中规模验证的有效方法，使对估计因素的探索性和验证性分析成为可能，并且还允许分析师通过使用可信区间插入先验信息，而不管样本大小对于因子载荷或通过进行特定的假设检验。由于选择使用先验分布，因子分析中用作唯一性和公共性的主要估计值通常会失去其通常的解释，这抵消了贝叶斯方法的灵活性。原创性/价值——考虑到通过因子分析开发量表旨在促进管理中的适当决策以及在组织研究中越来越多地误用有序量表作为间隔，该建议似乎对混合数据分析有效。此处发现的发现并非旨在成为结论性或限制性的，而是提供了一个有用的起点，从中可以建立贝叶斯因子分析的进一步理论和实证研究。