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Factorial Analysis is an experimental design that applies Analysis of Variance (ANOVA) statistical procedures to examine a change in a dependent variable due to more than one independent variable, also known as factors. Changes in worker productivity can be reasoned, for example, to be influenced by salary and other conditions, such as skill level. One way to test this hypothesis is by categorizing salary into three levels (low, moderate, and high) and skills sets into two levels (entry level...
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Related Experiment Video

Updated: Mar 26, 2026

Machine Learning-Based Cough Tone Classification: Diagnostic Exploration of Chronic Obstructive Pulmonary Disease and Respiratory Tract Infections
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On The Robustness Of Factor Analysis Against Crude Classification Of The Observations.

U Olsson

    Multivariate Behavioral Research
    |January 26, 2016
    PubMed
    Summary

    Ordinal data with few scale steps can distort factor analysis. Classification of true variables may erroneously suggest more factors are needed and attenuate loading estimates in maximum likelihood factor analysis.

    Area of Science:

    • Statistics
    • Psychometrics
    • Data Analysis

    Background:

    • Maximum likelihood factor analysis (MLFA) assumes continuous observed variables.
    • Ordinal variables with few scale steps are common in social and behavioral sciences.
    • Classification of continuous variables into ordinal categories can impact statistical models.

    Purpose of the Study:

    • To investigate the consequences of using ordinal variables with few scale steps in MLFA.
    • To examine how classification of underlying continuous variables affects factor analysis results.
    • To understand the impact on model fit and parameter estimation.

    Main Methods:

    • Simulating data from a multivariate normal distribution with an underlying factor model.
    • Classifying true variables into ordinal variables with varying numbers of scale steps.

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  • Analyzing the classified data using MLFA and comparing results to the true model.
  • Investigating the effects of variable skewness and factor loadings.

    • Main Results:

    • Classification can lead to a substantial lack of model fit, suggesting a need for more factors.
    • This effect is pronounced with oppositely skewed variables and high true loadings.
    • Loading estimates are attenuated, with the effect increasing as the number of scale steps decreases.
    • The degree of attenuation is exacerbated by greater variation in skewness among variables.

    Conclusions:

    • Using few-step ordinal variables in MLFA can yield misleading results regarding model complexity.
    • Factor loading estimates are systematically biased downwards.
    • Researchers should be cautious when applying MLFA to sparsely categorized ordinal data.