missalpha: Find Range of Cronbach Alpha with a Dataset Including Missing
Data
Provides functions to calculate the minimum and maximum possible
values of Cronbach's alpha when item-level missing data are present.
Cronbach's alpha (Cronbach, 1951 <doi:10.1007/BF02310555>) is one of the most widely used
measures of internal consistency in the social, behavioral, and medical sciences
(Bland & Altman, 1997 <doi:10.1136/bmj.314.7080.572>; Tavakol & Dennick, 2011
<doi:10.5116/ijme.4dfb.8dfd>). However, conventional implementations assume
complete data, and listwise deletion is often applied when missingness occurs,
which can lead to biased or overly optimistic reliability estimates (Enders, 2003
<doi:10.1037/1082-989X.8.3.322>). This package implements computational strategies
including enumeration, Monte Carlo sampling, and optimization algorithms
(e.g., Genetic Algorithm, Differential Evolution, Sequential Least Squares
Programming) to obtain sharp lower and upper bounds of Cronbach's alpha under
arbitrary missing data patterns. The approach is motivated by Manski's partial
identification framework and pessimistic bounding ideas from optimization literature.
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