Multiple Classification Analysis Using SPSS

Multiple Classification Analysis using SPSS Widyo Pura Buana

Widyo Pura Pura Buana Buana - MCA

TEKNIK VARIABEL TERPENGARUH / VARIABEL DEPENDEN DEPEN DEN VA VARIAB RIABEL EL (Y)

ANALISIS DATA VARIABEL VARIAB EL PENGARUH / INDEPENDEN INDEPENDEN VARIABEL VARIABEL (X) NOMINAL

Dikotomi NOMINAL

Dikotomi

1. 2. 3. 4.

Difference of proportion test Chi-square Fish Fishe ers rs ex exact act tes testt Phi coefficie cient

Poli Polittomi omi

1. 1. 2.

ChiChi-sq squa uarre Kendalls VCT

ORDINAL

1. 2.

Man-Whitney Smirnov-Kolmogoronov

INTERVAL

1. 2.

Analysis of variance Diff Differen erence ce of of mean meanss test test (Sch (Schef effe fe test) Sign test M-test U-test Cros Crosss-cla class ssif ific icat atio ion n anal analys ysis is

3. 4. 5. 6.


Politomi

1. 2.

Chi-square Kendalls VCT

1.

Anal Analys ysis is of of var varia iance nce wit with h inte interc rcla lass correlation Dumm Dummy y varia ariabl ble es mult multip iple le regression Mult Multip iple le clas classi sific ficat atio ion n anal analys ysis is Cros Crosss-cla class ssif ific icat atio ion n anal analys ysis is

2. 3. 4.

TEKNIK VARIABEL TERPENGARUH / VARIABEL DEPENDEN DEPEN DEN VA VARIAB RIABEL EL (Y)

ANALISIS DATA VARIABEL VARIAB EL PENGARUH / INDEPENDEN INDEPENDEN VARIABEL VARIABEL (X) NOMINAL

Dikotomi NOMINAL

Dikotomi

1. 2. 3. 4.

Difference of proportion test Chi-square Fish Fishe ers rs ex exact act tes testt Phi coefficie cient

Poli Polittomi omi

1. 1. 2.

ChiChi-sq squa uarre Kendalls VCT

ORDINAL

1. 2.

Man-Whitney Smirnov-Kolmogoronov

INTERVAL

1. 2.

Analysis of variance Diff Differen erence ce of of mean meanss test test (Sch (Schef effe fe test) Sign test M-test U-test Cros Crosss-cla class ssif ific icat atio ion n anal analys ysis is

3. 4. 5. 6.


Politomi

1. 2.

Chi-square Kendalls VCT

1.

Anal Analys ysis is of of var varia iance nce wit with h inte interc rcla lass correlation Dumm Dummy y varia ariabl ble es mult multip iple le regression Mult Multip iple le clas classi sific ficat atio ion n anal analys ysis is Cros Crosss-cla class ssif ific icat atio ion n anal analys ysis is

2. 3. 4.

TEKNIK VARIABEL TERPENGARUH / DEPENDEN VARIABEL (Y) NOMINAL

Dikotomi

ANALISIS DATA

VARIABEL PENGARUH / INDEPENDEN VARIABEL VARIABEL (X) ORDINAL

1. Kruskall-Wallis 2. Frie Friedma dman nss 2 way way analy analysi siss of var varia ianc nce e

Politomi ORDINAL

1. Rank-order correlation 2. Kendalls tau 3. Gamma 4. Coef Coeffi fici cien entt of conc concor orda danc nce e

INTERVAL

Ubah var ordinal ja jadi var nominal & pakai analysis of variance, DVM R, MCA atau Ubah var interval Jadi var ordinal & pakai statistik statistik non-parametrik


TEKNIK VARIABEL TERPENGARUH / DEPENDEN VARIABEL (Y) NOMINAL

Dikotomi

ANALISIS DATA

VARIABEL PENGARUH / INDEPENDEN VARIABEL (X) INTERVAL

1. Logistic multiple regression 2. 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. 2. 3. 4.

Correlation atau regression Multiple correlation atau multiple regression Path analysis Partial regression

Widyo Pura Buana - MCA

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. Widyo Pura Buana - MCA

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

I ndependent

variables Statistical techniques

One

Several

Interval scale

Interval scale

Multiple Regression

Interval scale

Nominal

Multiple Classification Analysis

Dichotomous,

Nominal

Multiple Classification Analysis

Polytomous Widyo Pura Buana - MCA

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. Widyo Pura Buana - MCA

Model MCA Y ij...n=

Y + a i +b j+ . . . .+e ij..n

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

Y

= Grand mean of the dependent variable.

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


Model MCA Y ij ...n ! Grand Mean  Row Effect  Column Effect  Residual

Grand Mean

Y ij ...n !

Row Effect

Column Effect Residual


Performance by Task Difficulty and Arousal

Arousal (Column) Low Task Difficulty (Row)

Easy

Difficult

Column Mean

Medium High

3

2

9

1

5

9

1

9

13

6

7

6

4

7

8

0

3

0

2

8

0

0

3

0

0

3

5

3

3

0

2

5

5


Row Mean

6

2

4

Grand Mean

2

3

SS Total ! §§ ( yij  Y ) 2 i !1 j !1

! (3 - 4) 2  ...  (0  4) 2 ! 360 2

SS o ! §

2  ( y Y ) i i.

i !1 2

2

! 15.(6  4)  15.( 2  4) ! 30  30 ! 60 3

SS olu

n

!§

j ( y. j  Y )

2

j !1 2

2

! 10.( 2  4)  10.(5  4)  10.(5  4) ! 40  10  10 ! 60 Widyo Pura Buana - MCA

2

! SS o  SS C olu

n

SS Model ! SS o  SS C olu

n

SS C o

bined

SS R e sidual ! SS otal  SS Model Widyo Pura Buana - MCA

df Total ! N  1 ! 30  1 ! 29 df o ! # of ro s (levels)  1 ! 2  1 ! 1 df C olu

n

! # of colu ns (levels)  1 ! 3  1 ! 2

df Combined ! df Row  df Column ! 1  2 ! 3

df Model ! df Row  df Column ! 1  2 ! 3 df Re sidual ! df Total  df Model ! 29  3 ! 26 Widyo Pura Buana - MCA

Eta

(L)

Etarow ! L row !

Etacolumn ! L column ! Widyo Pura Buana - MCA

SS Row SS Total SS Column SS Total

Goodness of Fit

R  Squared !

!

SS Model SS Total

 Squared ! Widyo Pura Buana - MCA

SS

odel

SS T otal

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 Tingkat Kesulitan Pekerjaan

dan Gairah Kerja berpengaruh terhadap Performance Kerja (baik secara overall atau individual)

Performance

Experimental Method Sum of Squares 180.000

3

Mean Square 60.000

120.000

1

60.000

Model

8.667

Sig. .000

120.000

17.333

.000

2

30.000

4.333

.024

180.000

3

60.000

8.667

.000

Residual

180.000

26

6.923

Total

360.000

29

12.414

Main Effects

(Combined) Task Difficulty Arousal

df

a. Performance by Task Difficulty, Arousal


F

Significant

MCAa Predicted Mean Adjusted

N

Performance

Task Difficulty

Arousal

Deviation

Unadjusted

Adjusted

for Unadjusted Factors 6.00 2.000

for Factors 2.000

Easy

15

6.00

Difficult

15

2.00

2.00

-2.000

-2.000

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 Deviation Mean Row

Column

Task

Difficulty Arousal

Easy Difficult Low Medium High Grand

Mean

6

±4 =2±4 =2±4 =5±4 =5±4

2 =6

2

-2

2

-2

5

1

5

1

4


Row(i)-Grand

Mean

Column(j)-Grand Mean

Factor

Summarya Eta

Beta Adjusted for Factors

Task

Difficulty Performance (Row) Arousal (Column)

.577

.577

Formula =SQ RT( SSRow/ SSTotal ) =SQRT(120/360)

.408

.408


=SQ RT( SSColumn/ SSTotal ) =SQRT(60/360)

Model Goodness of Fit R

Performance by Task Difficulty, Arousal

R

Squared

.707

.500

=SQ RT(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

Performance

Main Effects

(Combined) Task Difficulty

2-Way

Interactions Model Residual Total

Sum of Squares 180.000

Experimental Method Mean Square df F 3 60.000 12.000

Sig. .000

120.000

1

120.000

24.000

.000

Arousal

60.000

2

30.000

6.000

Task

60.000

2

30.000

6.000

.008 .008

240.000

5

48.000

9.600

.000

120.000

24

5.000

360.000

29

12.414

Difficulty * Arousal


Graphical display of interactions Two

ways to display previous results iffic lt

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MCA $ GLM Factorial Anova


MCA $ GLM Factorial Anova MULTIPLE CLASSIFICATION ANALYSIS (MCA) Melissa A. Hardy & Chardie L. Baird

MULTIPLE CLASSIFICATION ANALYSIS (MCA) Also called factorial A NOVA, 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 C OVARIATE(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

The lines are parallel

Interaction Widyo Pura Buana - MCA

The

lines are not parallel

GLM Factorial ANOVA Statistical

Model:

Y ijk ! Q  E i  F j  EF ij  I k ( ij ) Statistical Hypothesis:

Treatment A. H 0 : E1 ! E 2 ! L ! E p Treatment B. H 0 : F1 ! F 2 ! L ! F q Interaction. H 0 : EF11 ! EF12 ! L ! EF pq The interaction null is that the cell means d o not differ significantly (fr om the grand mean) outside of the main effects present, i.e. that this residual effect is zer o Widyo Pura Buana - MCA





Multiple Classification Analysis Using SPSS

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