CONCEPTS TO BE INCLUDED Items Factor analysis Data reduction / scale construction Factors/dimensions Factor loadings

Factor analysis and factor loadings

AIM Reducing a set of (survey) items to a limited set of factors or dimensions, to create a few more abstract scales = Factor analysis Factor loadings

EXAMPLE: THE BIG FIVE NEO-PI-R personality scales measure five domains of personality Give an assessment of normal adult personality Are used in personality assessment

EXAMPLE: THE BIG FIVE Five constructs/dimensions/factors: Openness (closed minded – intellectual curiosity) Conscientiousness (sloppy/unreliable – highly organized) Extraversion (reflective – attention seeking) Agreeableness (suspicious – compassionate) Neuroticism (emotionally stable – emotionally unstable)

ITEMS MEASURING ONE CONSTRUCT: NEUROTICISM Neuroticism (emotionally stable – emotionally unstable) Items: “Even minor annoyances can be frustrating to me” “Sometimes I feel completely worthless” Strongly Disagree Disagree Neutral Agree Strongly agree 1 2 3 4 ◻️

A DATA MATRIX Respondent Item 1 Item 2 Etc… 1 2 (= neutral) 2 4 (= strongly agree) 4 3 0 (= strongly disagree) 5 6 7 8 9

Item 1 Concept correlation NOT directly observed Item 2

Neuroticism If the two items are indications of neuroticism, the answers will be correlated. Even minor annoyances can be frustrating to me Neuroticism correlation Sometimes I feel completely worthless

WHAT IS ‘FACTOR ANALYSIS’? A method to check whether a latent factor is able to account for the correlation between a set of items Latent factor (a.k.a. ‘dimension’) is here neuroticism

Neuroticism Even minor annoyances can be frustrating to me Then: correlation = 1 Neuroticism Suppose: corr. = 1 perfect correlation Sometimes I feel completely worthless Then: correlation = 1

ONE FACTOR REPLACES TWO ITEMS Item 1 = 1*Factor(N) Item 2 = 1*Factor(N) Item 1 Concept Factor loadings Item 2

ONE FACTOR REPLACES TWO ITEMS, WITH ERROR Item 1 = a * Factor(N) + Error Item 2 = b * Factor(N) + Error Then: correlation is between 0.81 and 1 Item 1 error Correlation = 0.81 Concept error Item 2 Then: correlation is between 1 and 0.81

FACTOR LOADING The extent to which a factor is able “to explain” an item is called a factor loading Item 1 = a * Factor(N) + error Item 2 = b * Factor(N) + error In this example factor loadings are between 1 and 0,81

INTERPRETING FACTOR LOADINGS A factor loading indicates how well a factor is able to explain an item A low factor loading indicates that the item does ‘not belong’ to the factor (= dimension, scale, construct) A high factor loading indicates the item belongs to the factor

FACTOR ANALYSIS Normally not just two, but many items Often not just one, but two or even more factors Factors ‘summarize’ a large set of ‘items’ into a smaller set of ‘variables’ (= dimensions, constructs)

FACTOR ANALYSIS If there IS an underlying factor, we could add the answers to the items and use that as one single variable measuring the construct Some items belong to a factor, whereas others do less

ONE FACTOR REPLACES TWO ITEMS, WITH ERROR Item 1 = 0.8 * Factor(N) + Error Item 2 = 0.9 * Factor(N) + Error Item 1 error 0.8 Factor loadings Corr. = 0.72 Concept error Item 2 0.9

( x ) + ( + ) = = A DATA MATRIX Resp Factor loading item 1 Item 1 Scale 1 0,8 0,9 2 2,7 4 3 6 5 7 8 9 ( x ) + ( + ) = =

THIS MICROLECTURE A set of (survey) items can be reduced to a limited set of factors or dimensions, creating a few more abstract scales This is done using factor analysis Factor analysis gives you factor loadings, which can be used to create a summated scale