Multiple Classification Analysis (MCA)

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Multiple Regression dan Multiple Classification Analysis

MCA analisis multivariat dg beberapa variabel bebas (indep. vbl) dan satu variabel tidak bebas (dependent vbl) dg tujuan :

• Mengetahui seberapa besar pengaruh indep vbl secara bersama sama thdp dependent vbl

• Mengetahui seberapa besar pengaruh setiap indep vbl thdp dependent vbl baik mempertimbangkan efek indep vbl yang lain maupun mengabaikan efek indep vbl yang lain

• Persamaan additive• Perbedaan Multipel Regresi dan MCA

Dependent variable

One

Independent variables

Several

Statistical techniques

Interval scale Interval scale Multiple Regression

Interval scale Nominal Multiple Classification Analysis

Dichotomous,

Polytomous

Nominal Multiple Classification Analysis

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

Dimana

Yij...n = skor dependent variable utk individu n yg berada pada kategori i dari prediktor A, kategori j dari prediktor B, dst.

= rata-rata keseluruhan (Grand mean) dependent variabel.

ai = efek kategori ke - i dari prediktor A. bj = efek kategori ke - j dari prediktor B. e ij..n= error utk individu ybs.

Y

Y

Model MCA

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Model MCA Residual ... EffectColumnEffectRowMeanGrandY nij

nijY ...

Grand Mean

Row Effect

Column Effect

Residual

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... nijY Rata-rata keseluruhan + Efek baris + efek kolom + sisaan

Contoh : 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

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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

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ColumnRowCombined SSSSSS

ColumnRowModel SSSSSS

ModelTotalsidual SSSSSS Re

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321 ColumnRowCombined dfdfdf

321 ColumnRowModel dfdfdf

291301 NdfTotal

26329Re ModelTotalsidual dfdfdf

1121)( # levelsrowsofdfRow2131)( # levelscolumnsofdfColumn

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Total

Rowrowrow SS

SSEta

Total

Columncolumncolumn SS

SSEta

Eta ()

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Goodness of Fit

Total

Model

SS

SSSquaredRR

Total

Model

SS

SSSquaredR

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

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Struktur Data MCA dengan SPSS

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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)

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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

RowTask

DifficultyEasy 6 2 = 6 – 4

Row(i)-Grand MeanDifficult 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  

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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)

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Model Goodness of Fit R R Squared

Performance by Task Difficulty, Arousal .707 .500

=SQRT(R-Squared) = SSModel/SSTotal

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Contoh lain Multiple Classification Analysis

Jabatan Akademitk:-Tidakada - Asisten Ahli (AA) - Lektor

Jenis Kelamin:

- Laki‐Laki ( L) - Perempuan (P)

Golongan :-III (3) -IV (4)

Gaji yang diterima - Rp. 2 juta - Rp. 3 juta - Rp. 4 juta - Rp. 5 juta

1.Jabatan Akademik Lektor menunjukkan Adjusted Mean paling besar. Artinya Tingkat Jabatan Akademik yang lebih tinggi akan berpengaruh untuk mendapatkan gaji yang lebih besar 2. Dosen laki-laki yang mempunyai Jabatan Akademik Lektor dan masuk dalam Golongan Kepegawaian IV memiliki peluang gaji yang lebih besar 3. Jabatan Akademik berpengaruh terhadap “Rata-rata Gaji yang diterima” secara signifikan 4. Jenis kelamin berpengaruh terhadap “Rata-rata Gaji yang diterima” secara signifikan. 5. Golongan Kepegawaian berpengaruh terhadap “Rata-rata Gaji yang diterima” secara signifikan 6. Jabatan Akademik, Jenis kelamin, Golongan Kepegawaian secara bersama-sama berpengaruh signifikan terhadap “Rata-rata Gaji yang diterima” yaitu sebesar = 85,078 % dan sebesar 14,921 % dipengaruhi oleh faktor lain

Multiple Classification Analysis with Interaction

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

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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    

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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

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