gilles raîche, martin riopel, jean-guy blais non graphical solutions for the cattells scree test...
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Gilles Raîche, Martin Riopel, Jean-Guy Blais
Non Graphical Solutions for the Cattell’s Scree Test
Gilles Raîche, UQAM
Martin Riopel, UQAM
Jean-Guy Blais, Université de Montréal
Montréal
June 16th 2006
Gilles Raîche, Martin Riopel, Jean-Guy Blais
STEPS Scree test weekness Classical strategies for the number
of components to retain Non graphical solutions for the scree
test
Gilles Raîche, Martin Riopel, Jean-Guy Blais
Scree Test Weekness
Figural non numeric solution Subjectivity Low inter-rater agreement (from a
low 0.60, mean of 0.80)
Gilles Raîche, Martin Riopel, Jean-Guy Blais
Classical Strategies for the Number of Components to Retain
Kaiser-Guttman rule
)1( iGK Countn
2 4 6 8 10
0.5
1.0
1.5
2.0
2.5
3.0
Component
Eig
en
valu
e
Gilles Raîche, Martin Riopel, Jean-Guy Blais
Classical Strategies for the Number of Components to Retain
Parallel Analysis
i. Generate n random observations according to a N(0,1) distribution independently for p variates
ii. Compute the Pearson correlation matrixiii. Compute the eigenvalues of the Pearson correlation
matrixiv. Repeat steps 1 to 3 k timesv. Compute a location statistic () on the p vectors of k
eigenvalues : mean, median, 5th centile, 95th centile, etc.
vi. Replace the value 1.00 by the location statistic in the Kaiser-Guttman formula.
Gilles Raîche, Martin Riopel, Jean-Guy Blais
Classical Strategies for the Number of Components to Retain
Parallel Analysis
)( iiParallel LSCountn
2 4 6 8 10
0.5
1.0
1.5
2.0
2.5
3.0
Component
Eig
en
valu
e
Gilles Raîche, Martin Riopel, Jean-Guy Blais
Classical Strategies for the Number of Components to Retain
Cattell’s Scree Test
2 4 6 8 10
0.5
1.0
1.5
2.0
2.5
3.0
Scree test
Component
Eig
en
valu
e
Gilles Raîche, Martin Riopel, Jean-Guy Blais
Non Graphical Solutions to the Scree Test
Optimal Coordinates
)(( and )1(Count iiioc predictedn
)(( and )(Count iiiioc predictedLSn
Gilles Raîche, Martin Riopel, Jean-Guy Blais
Non Graphical Solutions to the Scree Test
Acceleration Factor
h
hififhifif
)()(2)()(''
)1()(2)1()('' ifififif
)max(( and )1( If afin iaf
)max(( and )( If afiLSn iiaf
Gilles Raîche, Martin Riopel, Jean-Guy Blais
Non Graphical Solutions to the Scree Test
Example I
2 4 6 8 10
0.5
1.0
1.5
2.0
2.5
3.0
Component
Eig
en
valu
e
Eigenvalues ........(nkeyser = 4 )Parallel Analysis ..(n = 2 )Optimal Coordinates (n = 2 )Acceleration factor (n = 2 )
Gilles Raîche, Martin Riopel, Jean-Guy Blais
Non Graphical Solutions to the Scree Test
Component Eigenvalue Parallel Analysis
Optimal Coordinate
AccelerationFactor
123456789
1011
3.122.701.221.160.880.760.700.590.450.400.35
2.151.751.471.261.050.890.760.620.480.350.23
2.961.331.28nananananananana
na-1.061.42nananananananana
Gilles Raîche, Martin Riopel, Jean-Guy Blais
Conclusion Parsimonious solutions Easy to implement More comparisons have to be done
with other solutions
Gilles Raîche, Martin Riopel, Jean-Guy Blais
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http://www.er.uqam.ca/nobel/r17165/
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