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首页> 外文期刊>Open Journal of Statistics >Testing Rating Scale Unidimensionality Using the Principal Component Analysis (PCA)/t-Test Protocol with the Rasch Model: The Primacy of Theory over Statistics
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Testing Rating Scale Unidimensionality Using the Principal Component Analysis (PCA)/t-Test Protocol with the Rasch Model: The Primacy of Theory over Statistics

机译：使用主成分分析（PCA）/ t检验协议和Rasch模型检验等级量表的一维性：理论对统计的重要性

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Psychometric theory requires unidimensionality (i.e., scale items should represent a common latent variable). One advocated approach to test unidimensionality within the Rasch model is to identify two item sets from a Principal Component Analysis (PCA) of residuals, estimate separate person measures based on the two item sets, compare the two estimates on a person-by-person basis using t-tests and determine the number of cases that differ significantly at the 0.05-level; if ≤5% of tests are significant, or the lower bound of a binomial 95% confidence interval (CI) of the observed proportion overlaps 5%, then it is suggested that strict unidimensionality can be inferred; otherwise the scale is multidimensional. Given its proposed significance and potential implications, this procedure needs detailed scrutiny. This paper explores the impact of sample size and method of estimating the 95% binomial CI upon conclusions according to recommended conventions. Normal approximation, “exact”, Wilson, Agresti-Coull, and Jeffreys binomial CIs were calculated for observed proportions of 0.06, 0.08 and 0.10 and sample sizes from n= 100 to n= 2500. Lower 95%CI boundaries were inspected regarding coverage of the 5% threshold. Results showed that all binomial 95% CIs included as well as excluded 5% as an effect of sample size for all three investigated proportions, except for the Wilson, Agresti-Coull, and JeffreysCIs, which did not include 5% for any sample size with a 10% observed proportion. The normal approximation CI was most sensitive to sample size. These data illustrate that the PCA/t-test protocol should be used and interpreted as any hypothesis testing procedure and is dependent on sample size as well as binomial CI estimation procedure. The PCA/t-test protocol should not be viewed as a “definite” test of unidimensionality and does not replace an integrated quantitative/qualitative interpretation based on an explicit variable definition in view of the perspective, context and purpose of measurement.
机译：心理计量学理论要求具有一维性（即，比例尺项目应代表一个共同的潜在变量）。在Rasch模型中测试一维性的一种提倡方法是从残差的主成分分析（PCA）中识别出两个项目集，根据这两个项目集估计单独的人为度量，并逐人比较这两个估计值使用t检验并确定在0.05水平上有显着差异的病例数;如果≤5％的检验显着，或者所观察比例的二项式95 %%置信区间（CI）的下限重叠5％，则建议可以推断出严格的一维性;否则规模是多维的。鉴于其拟议的重要性和潜在的影响，此过程需要详细的审查。本文探讨了样本量的影响以及根据建议的约定对得出结论的95％二项式CI进行估计的方法。对于观察到的比例0.06、0.08和0.10以及样本量从n = 100到n = 2500，计算正态近似，“精确”，Wilson，Agresti-Coull和Jeffreys二项式CI，计算覆盖率较低的95 ％CI边界阈值的5％。结果表明，对于所有三个调查比例，所有二项式95％CI都包括进来，而排除了5％，威尔逊，Agresti-Coull和JeffreysCI除外，后者不包括5％样本量，观察比例为10％。正常近似CI对样本大小最敏感。这些数据表明，应该使用PCA / t检验协议并将其解释为任何假设检验程序，并且取决于样本量以及二项式CI估计程序。 PCA / t-test协议不应被视为一维的“确定性”测试，并且鉴于测量的角度，背景和目的，也不能代替基于显式变量定义的综合定量/定性解释。

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