Multiple Classification Analysis Using SPSS

Widyo Pura Buana - MCA

Multiple Classification Analysis using SPSS

Widyo Pura Buana


TEKNIK ANALISIS DATAVARIABEL TERPENGARUH /

DEPENDEN VARIABEL (Y)VARIABEL PENGARUH / INDEPENDEN VARIABEL (X)

NOMINAL

Dikotomi Politomi

NOMINAL Dikotomi 1. Difference of proportion test2. Chi-square3. Fisher’s exact test4. Phi coefficient

Politomi 1. Chi-square2. Kendall’s VCT

1. Chi-square2. Kendall’s VCT

ORDINAL 1. Man-Whitney2. Smirnov-Kolmogoronov

INTERVAL 1. Analysis of variance2. Difference of means test (Scheffe

test)3. Sign test4. M-test5. U-test6. Cross-classification analysis

1. Analysis of variance with interclas correlation

2. Dummy variables multiple regression

3. Multiple classification analysis4. Cross-classification analysis


TEKNIK ANALISIS DATA

VARIABEL TERPENGARUH /

DEPENDEN VARIABEL (Y)

VARIABEL PENGARUH / INDEPENDEN VARIABEL (X)ORDINAL

NOMINAL Dikotomi 1. Kruskall-Wallis2. Friedman’s 2 way analysis of variance

Politomi ORDINAL 1. Rank-order correlation

2. Kendall’s tau3. Gamma4. Coefficient of concordance

INTERVAL Ubah var ordinal jadi var nominal & pakai analysis of variance, DVMR, MCA atau Ubah var interval Jadi var ordinal & pakai statistik non-parametrik


TEKNIK ANALISIS DATA

VARIABEL TERPENGARUH /

DEPENDEN VARIABEL (Y)

VARIABEL PENGARUH / INDEPENDEN VARIABEL (X)INTERVAL

NOMINAL Dikotomi 1. Logistic multiple regression2. Discriminant analysis

Politomi ORDINAL Ubah var ordinal jadi var nominal & pakai logistic

multiple regression & discriminant analysis atau Ubah var interval jadi var ordinal & pakai statistik non-parametrik

INTERVAL 1. Correlation atau regression2. Multiple correlation atau multiple regression3. Path analysis4. Partial regression


Multiple Regression and Multiple Classification Analysis

Introduction• This chapter examines a model of multivariate analysis,

involving simultaneous consideration of several independent (predictor or explanatory) variables and one dependent variable, where the objectives of analysis are:(i) To know how well all the independent variables together explain variation in the dependent variable.(ii) To know how well each independent variable is related to the dependent variable, either considering or ignoring the effects of other independent variables.


Multiple Regression and Multiple Classification Analysis

• The following data analysis situations can be visualized, depending upon the measurement properties of the dependent and independent variables.

Dependent variable One

Independent variablesSeveral

Statistical techniques

Interval scale Interval scale Multiple Regression Interval scale Nominal Multiple Classification Analysis Dichotomous, Polytomous

Nominal Multiple Classification Analysis


Multiple Classification Analysis (MCA)

• Multiple Classification Analysis (MCA) is a technique for examining the interrelationship between several predictor variables and one dependent variable in the context of an additive model.

• Unlike simpler forms of other multivariate methods, MCA can handle predictors with no better than nominal measurements and interrelationships of any form among the predictor variables or between a predictor and dependent variable. It is however essential that the dependent variable should be either an interval-scale variable without extreme skewness or a dichotomous variable with frequencies which are not extremely unequal.


Yij...n= + ai +bj+ . . . .+e ij..n

whereYij...n = The score on the dependent variable of individual n who falls in category i of predictor A, category j of predictor B, etc

= Grand mean of the dependent variable.

ai = The effect of the membership in the i th category of predictor A.bj = The effect of the membership in the j th category of predictor B. e ij..n= Error term for this individual.

Y

Y

Model MCA


Model MCA Residual ... EffectColumnEffectRowMeanGrandY nij

nijY ...

Grand Mean

Row Effect

Column Effect

Residual


Performance by Task Difficulty and Arousal

Arousal (Column)Row Mean

Low Medium High

Task Difficulty

(Row)

Easy 3 2 9

6

1 5 9

1 9 13

6 7 6

4 7 8

Difficult 0 3 0

22 8 00 3 00 3 53 3 0

Column Mean 2 5 5 4 Grand Mean


360)40(...4)-(3

)(

22

2

1

23

1

i

ijj

Total YySS

603030 )42.(15)46.(15

)(

22

2

1

2.

i

iiRow YywSS

60101040

)45.(10)45.(10)42.(10

)(

222

3

1

2.

j

jjColumn YywSS


ColumnRowCombined SSSSSS

ColumnRowModel SSSSSS

ModelTotalsidual SSSSSS Re


321 ColumnRowCombined dfdfdf

321 ColumnRowModel dfdfdf

291301 NdfTotal

26329Re ModelTotalsidual dfdfdf

1121)( # levelsrowsofdfRow2131)( # levelscolumnsofdfColumn


Total

Rowrowrow SS

SSEta

Total

Columncolumncolumn SS

SSEta

Eta ()


Goodness of Fit

Total

Model

SS

SSSquaredRR

Total

Model

SS

SSSquaredR


Syntax SPSS MCA *MCA model with categorical predictors:.ANOVA Performance by Difficulty (1,2) Arousal (1,3) /MAXORDERS=NONE/METHOD=EXPERIMENTAL/STATISTICS=MCA.


Struktur Data MCA dengan SPSS


ANOVAa

Experimental Method

Sum of Squares df

Mean Square F Sig.

Performance Main Effects

(Combined) 180.000 3 60.000 8.667 .000

Task Difficulty 120.000 1 120.000 17.333 .000

Arousal 60.000 2 30.000 4.333 .024

Model 180.000 3 60.000 8.667 .000

Residual 180.000 26 6.923 Total 360.000 29 12.414

a. Performance by Task Difficulty, Arousal

Significant

Tingkat Kesulitan Pekerjaan dan Gairah Kerja berpengaruh terhadap Performance Kerja

(baik secara overall atau individual)


MCAa

N

Predicted Mean Deviation

UnadjustedAdjusted

for Factors

UnadjustedAdjusted

for Factors

Performance Task Difficulty Easy 15 6.00 6.00 2.000 2.000

Difficult 15 2.00 2.00 -2.000 -2.000

Arousal Low 10 2.00 2.00 -2.000 -2.000

Medium 10 5.00 5.00 1.000 1.000

High 10 5.00 5.00 1.000 1.000

a. Performance by Task Difficulty, Arousal

Performance

DeviationMean

Row Task Difficulty

Easy 6 2 = 6 – 4Row(i)-Grand Mean

Difficult 2 -2 = 2 – 4

Column ArousalLow 2 -2 = 2 – 4

Column(j)-Grand MeanMedium 5 1 = 5 – 4High 5 1 = 5 – 4

Grand Mean 4


Factor Summarya

EtaBeta

FormulaAdjusted for Factors

Performance

Task Difficulty (Row)

.577 .577=SQRT( SSRow/ SSTotal )

=SQRT(120/360)

Arousal (Column)

.408 .408=SQRT( SSColumn/ SSTotal )

=SQRT(60/360)


Model Goodness of Fit R R Squared

Performance by Task Difficulty, Arousal .707 .500

=SQRT(R-Squared) = SSModel/SSTotal


Multiple Classification Analysis with Interaction


Syntax SPSS MCA *MCA model with categorical predictors, interaction:.ANOVA Performance by Difficulty (1,2) Arousal (1,3) /MAXORDERS=ALL/METHOD=EXPERIMENTAL/STATISTICS=MCA.


ANOVAa

Experimental Method

Sum of Squares df

Mean Square F Sig.

Performance Main Effects (Combined) 180.000 3 60.000 12.000 .000

Task Difficulty 120.000 1 120.000 24.000 .000

Arousal 60.000 2 30.000 6.000 .0082-Way Interactions

Task Difficulty * Arousal

60.000 2 30.000 6.000 .008

Model 240.000 5 48.000 9.600 .000Residual 120.000 24 5.000 Total 360.000 29 12.414


Graphical display of interactions

• Two ways to display previous results

lo med hi

Arousal

0.00

2.00

4.00

6.00

8.00

10.00

Mea

n S

core

Difficulty

difficult

easy

easy difficult

Difficulty

0.00

2.00

4.00

6.00

8.00

10.00

Mea

n S

core

Arousal

hi

lo

med


MCA GLM Factorial Anova


MCA GLM Factorial AnovaMULTIPLE CLASSIFICATION ANALYSIS (MCA) Melissa A. Hardy & Chardie L. Baird

MULTIPLE CLASSIFICATION ANALYSIS (MCA) Also called factorial ANOVA, multiple classification analysis (MCA) is a QUANTITATIVE analysis procedure that allows the assessment of differences in subgroup means, which may have been adjusted for compositional differences in related factors and/or covariates and their effects. MCA produces the same overall results as MULTIPLE REGRESSION with DUMMY VARIABLES, although there are differences in the way the information is reported. For example, an MCA in SPSS produces an ANALYSIS OF VARIANCE with the appropriate F TESTS, decomposing the SUMS OF SQUARES explained by the model into the relative contributions of the factor of interest, the COVARIATE(s), and any INTERACTIONS that are specified. These F tests assess the ratio of the sums of squares explained by the factor(s) and covariates (if specified) adjusted...

Source : http://srmo.sagepub.com/view/the-sage-encyclopedia-of-social-science-research-methods/n597.xml


Graphical display of interactions

• What are we looking for?• Do the lines behave similarly (are parallel) or

not?• Does the effect of one factor depend on the

level of the other factor?

No interaction Interaction

The lines are parallel The lines are not parallel


( )ijk i j k ijijY

0 1 2Treatment A. :

pH

0 1 2Treatment B. :

qH

0 11 12Interaction. :

pqH

Statistical Hypothesis:

Statistical Model:

GLM Factorial ANOVA

The interaction null is that the cell means do not differ significantly (from the grand mean) outside of the main effects present, i.e. that this residual effect is zero

Multiple Classification Analysis Using SPSS

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