Factor Analysis Flashcards

1
Q

What is Factor Analysis?

A
  • Factor Analysis is a family of techniques used to investigate the underlying structure of variables.
    • Determining whether many variables can be reduced to fewer, higher order (latent) variables (called factors)
    • Groups together highly correlated variables
  • Three main types:
    • Principle Components Analysis; data reduction technique (doesn’t extract factors. All items given same regression weight, creates components (not factors).
    • Exploratory Factor Analysis; Extract factors predicting the latent construct (items which covary together stay together), creates factors
    • Confirmatory Factor Analysis; when you already have a theory
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2
Q

What are the differences between EFA and CFA?

A
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3
Q

What are the three main uses of factor analysis according to Field?

A
  1. To understand the structure of a set of variables; such as investigating intelligence, wellbeing, personality and other complex constructs
  2. To develop a questionnaire to measure a variable; Factor analysis is often used to test the validity and internal structure of questionnaires
  3. To reduce a data set to a more manageable size while retaining the data set’s essential qualities; Especially when there are issues with multicollinearity, highly correlated variables can be condensed into factors
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4
Q

According to Fabringer et al. what 5 decisions need to be made when using factor analysis?

A
  1. Study Design and What variables are to be measured: Consider nature and number of common factors they wish to examine, ensure those factors are represented in multiple measurements
  2. Determine whether EFA is appropriate; goal of EFA is to produce a more parsimonious model of factors
  3. Choice of model fitting procedure (which factor extraction procedure to use)
  4. Numbers of factors: balancing parsimony with ability of model to account for correlations between variables (plausibility)
  5. Rotation Methods: whether to allow for correlations between factors
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5
Q

What are three ways of viewing relationships in factor analysis?

A
  • R-Matrix; a correlation table used to eyeball the data (look for groups of high correlations)
  • Plot; Presenting the proposed factors as axis on a graph, plot the correlation of each variable with the factor on the graph to reveal clusters.
    • Factor/Component Loading = coordinate of a variable along a classification axis (given by pearson correlation)
  • Mathematically; A matrix representation of the factor loadings
    • Column per factor, Row per variable
      *
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6
Q

What are the four methods of combining factor scores?

A
  • Weighted Average; rarely used because it is too simplistic.
    • Uses a linear model formula, sub in the individual’s scores
    • Cannot compare results across different measurements
  • Regression Method; more sophisticated but there are limits imposed on how scores can relate to each other
    • Generates coefficients adjusted for intial correlations between variables
    • Recommended for most circumstances
  • Bartlett Method; overcomes limits of regression by producing unbiased scores. Factor scores can still correlate with each other though.
  • Anderson-Rubin Method; modification of Bartlett method which produces uncorrelated and standardised factor scores
    • recommended when requiring standardised scores
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7
Q

What is Communality?

A
  • Communality is the proportion of common variance present in a variable
    • Empasse: FA requires knowledge of communality but you need to conduct FA to discover communality.
  • Determining Shared Variance:
    • PCA: Assume a value of 1 (no unique variance) for all variables
      • Problem; assumes no measurement error
    • Estimating Communality; many methods available eg
      • Squared Multiple Correlation (SMC); Run a multiple regression using one measure as outcome and others as predictors. R2 is used as a communality estimate for that factor
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8
Q

What are some different ways of extracting factors?

A
  • Eigenvalues; Represent the proportion of variance accounted for by a factor
  • Kaisers Criterion/Jiffy: Retain all factors with eigenvalues > 1
    • Overly simplistic- tends to over or under extract
    • Joliffe recommended .7 cutoff
  • Catells’ Scree Plot: Eigenvalues on Y axis, factor associated on x; look for the ‘elbow’ of the curve
    • Very subjective, up to researchers discretion
  • Monte Carlo Parallel Analysis; Similar process to bootstrapping - compares observed eigenvalues to average of many simulated data sets. Retain factors that exceed those expected
    • Underutilised since requires SPSS syntax
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9
Q

What is rotation and what are the different types?

A
  • Rotation is a technique which maximises an item’s loading on its primary factor while minimising loading on other factors
  • Orthogonal Rotation; Assume factors to be uncorrelated. Counter-intuitive for Psyc.
    • Varimax Rotation; Good starting point. Maximises dispersion to aid interpretation.
  • Oblique Rotation; Assumes factors to be correlated. All techniques produce similar results
    • Direct Quartimin; direct rotation
    • Direct Oblimin; direct rotation + predetermining degree of correlation
    • Promax; faster, uses orthogonal up to a point
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10
Q

What assumptions need to be met when conducting factor analysis?

A
  • Data Cleaning; inaccurate entries and missing data are important.
    • Missing data; cannot use listwise deletion when participants are answering 120 questions. Remember to check for patterns
  • Normality; Not strictly required but enhances factor structure
  • Linearity; Need to examine scatterplots for each pair of variables. Can be done more quickly using a scatterplot matrix.
  • Correlations; Create a correlation matrix for all the variables
    • Too Low: Consider excluding variables with several low (.3) correlations
      • Bartletts test; should be significant (otherwise it is essentially an identity matrix = disaster)
    • Too High; multicollinearity
      • Determinant of R-Matrix should be > .00001
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11
Q

What sample size is required for factor analysis?

A
  • Sample Size; Aim for 300 - 1000+ participants
    • Bare minimum is 5 participants per variable, more common recommendation is 10 - 15 per variable
  • Sample size can be less for factors with stronger loadings; if a factor has 4+ loadings > .6 it is reliable regardless of sample size
  • Kaiser Meyer Olken Measure of sampling adequacy (KMO)
    • Measures ratio of squared correlations between variables to squared partial correlations
    • Values below .5 = Merde, values >.9 = marvellous
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12
Q

How is reliability assessed in factor analysis?

A
  • Internal consistency is measured using Chronbach’s Alpha (measure of split half internal consistency)
  • Chronbach’s a; most commonly reported statistic, with values above .8 generally considered reliable. But:
    • a is biased by sample size
    • a is affected by reverse phrasing
    • a is not a measure of uni-dimensionality
    • Assumes uncorrelated errors multivariate normality, etc
  • SPSS: Check overall, corrected item column, if item deleted column.
    • Run separate analyses for each subscale
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