Factor Analysis & The Measurement Model
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Factor analysis is a statistical method used for data reduction, scale development, and evaluating psychometric measures by assessing the dimensionality of a set of variables. It identifies underlying latent constructs such as teaching effectiveness and motivation, simplifying the understanding of complex phenomena through measurement of various dimensions. The technique generates factors that represent these constructs, allowing for a clearer analysis of the data.
![Factor Analysis
6
Find a small number of factors z, which when combined
generate x :
xi – µi = vi1z1 + vi2z2 + ... + vikzk + εi
where zj, j =1,...,k are the latent factors with
E[ zj ]=0, Var(zj)=1, Cov(zi ,, zj)=0, i ≠ j ,
εi are the noise sources
E[ εi ]= ψi, Cov(εi , εj) =0, i ≠ j, Cov(εi , zj) =0 ,
and vij are the factor loadings](https://image.slidesharecdn.com/risilcentc-200327033351/85/Factor-Analysis-The-Measurement-Model-6-320.jpg)
Factor Analysis & The Measurement Model
- 1. Factor Analysis Prof. (Dr.) Risil Chhatrala Department of Electronics and Telecommunication International Institute of Information Technology, I²IT www.isquareit.edu.in 1
- 2. Factor Analysis Factor analysis is commonly used in: Data reduction Scale development The evaluation of the psychometric quality of a measure, and The assessment of the dimensionality of a set of variables. International Institute of Information Technology, I²IT, P-14, Rajiv Gandhi Infotech Park, Hinjawadi Phase 1, Pune - 411 057 Phone - +91 20 22933441/2/3 | Website - www.isquareit.edu.in | Email - info@isquareit.edu.in 2
- 3. Constructs : unobservable latent variables Teaching Effectiveness. Motivation Love Hate care Altruism Anxiety Worry Stress International Institute of Information Technology, I²IT, P-14, Rajiv Gandhi Infotech Park, Hinjawadi Phase 1, Pune - 411 057 Phone - +91 20 22933441/2/3 | Website - www.isquareit.edu.in | Email - info@isquareit.edu.in 3 product quality Physical aptitude democracy reliability/power.
- 4. construct may include several dimensions… Factor analysis measures not directly observable constructs by measuring several of its underlying dimensions. The identification of such underlying dimensions (factors) simplifies the understanding and description of complex constructs. International Institute of Information Technology, I²IT, P-14, Rajiv Gandhi Infotech Park, Hinjawadi Phase 1, Pune - 411 057 Phone - +91 20 22933441/2/3 | Website - www.isquareit.edu.in | Email - info@isquareit.edu.in 4
- 5. Factor Analysis: The Measurement Model D1 D8 D7D6 D5D4D3D2 F1 F2
- 6. Factor Analysis 6 Find a small number of factors z, which when combined generate x : xi – µi = vi1z1 + vi2z2 + ... + vikzk + εi where zj, j =1,...,k are the latent factors with E[ zj ]=0, Var(zj)=1, Cov(zi ,, zj)=0, i ≠ j , εi are the noise sources E[ εi ]= ψi, Cov(εi , εj) =0, i ≠ j, Cov(εi , zj) =0 , and vij are the factor loadings
- 7. Thank you!! 7 International Institute of Information Technology, I²IT, P-14, Rajiv Gandhi Infotech Park, Hinjawadi Phase 1, Pune - 411 057 Phone - +91 20 22933441/2/3 | Website - www.isquareit.edu.in | Email - info@isquareit.edu.in
- 8. Prof. (Dr.) Risil Chhatrala Associate Professor in Department of Electronics and Telecommunication International Institute of Information Technology (I²IT), Pune risilc@isquareit.edu.in 8 International Institute of Information Technology, I²IT, P-14, Rajiv Gandhi Infotech Park, Hinjawadi Phase 1, Pune - 411 057 Phone - +91 20 22933441/2/3 | Website - www.isquareit.edu.in | Email - info@isquareit.edu.in