Multiple Classification Analysis using SPSS Widyo Pura Buana Widyo Pura Buana - MCA TEKNIK ANALISIS DATA VARIABEL TERPENGARUH / DEPENDEN VARIABEL (Y) VARIABEL PENGARUH / INDEPENDEN VARIABEL (X) NOMINAL Dikotomi Politomi NOMINAL Dikotomi 1. Difference of proportion test 2. Chi-square 3. Fishers exact test 4. Phi coefficient Politomi 1. Chi-square 2. Kendalls VCT 1. Chi-square 2. Kendalls VCT ORDINAL 1. Man-Whitney 2. Smirnov-Kolmogoronov INTERVAL 1. Analysis of variance 2. Difference of means test (Scheffe test) 3. Sign test 4. M-test 5. U-test 6. Cross-classification analysis 1. Analysis of variance with interclas correlation 2. Dummy variables multiple regression 3. Multiple classification analysis 4. Cross-classification analysis Widyo Pura Buana - MCA TEKNIK ANALISIS DATA VARIABEL TERPENGARUH / DEPENDEN VARIABEL (Y) VARIABEL PENGARUH / INDEPENDEN VARIABEL (X) ORDINAL NOMINAL Dikotomi 1. Kruskall-Wallis 2. Friedmans 2 way analysis of variance Politomi ORDINAL 1. Rank-order correlation 2. Kendalls tau 3. Gamma 4. 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 Widyo Pura Buana - MCA TEKNIK ANALISIS DATA VARIABEL TERPENGARUH / DEPENDEN VARIABEL (Y) VARIABEL PENGARUH / INDEPENDEN VARIABEL (X) INTERVAL NOMINAL Dikotomi 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. Correlation atau regression 2. Multiple correlation atau multiple regression 3. Path analysis 4. 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 One Independent variables Several Statistical techniques Interval scale Interval scale Multiple Regression Interval scale Nominal Multiple Classification Analysis Dichotomous, Polytomous Nominal Multiple Classification Analysis 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 Yij...n= + ai +bj+ . . . .+e ij..n where Yij...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. YYModel MCA Widyo Pura Buana - MCA Model MCA Residual... + + + = Effect Column Effect Row Mean Grand Y n ij=n ijY...Grand Mean Row Effect Column Effect Residual Widyo Pura Buana - MCA 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 2 2 8 0 0 3 0 0 3 5 3 3 0 Column Mean 2 5 5 4 Grand Mean Widyo Pura Buana - MCA 360 ) 4 0 ( ... 4) - (3 ) (2 221231= + + = == = iijjTotal Y y SS60 30 30 ) 4 2 .( 15 ) 4 6 .( 15 ) (2 2212.= + = + = == ii i Row Y y w SS60 10 10 40 ) 4 5 .( 10 ) 4 5 .( 10 ) 4 2 .( 10 ) (2 2 2312.= + + = + + = == jj j Column Y y w SSWidyo Pura Buana - MCA Column Row Combined SS SS SS + =Column Row Model SS SS SS + =Model Total sidual SS SS SS =ReWidyo Pura Buana - MCA 3 2 1 = + = + = Column Row Combined df df df3 2 1 = + = + = Column Row Model df df df29 1 30 1 = = = N dfTotal26 3 29Re = = = Model Total sidual df df df1 1 2 1 ) ( # = = = levels rows of dfRow2 1 3 1 ) ( # = = = levels columns of dfColumnWidyo Pura Buana - MCA TotalRowrow rowSSSSEta = =qTotalColumncolumn columnSSSSEta = =qEta (q) Widyo Pura Buana - MCA Goodness of Fit TotalModelSSSSSquared R R = =TotalModelSSSSSquared R = Widyo Pura Buana - MCA Syntax SPSS MCA *MCA model with categorical predictors:. ANOVA Performance by Difficulty (1,2) Arousal (1,3) /MAXORDERS=NONE /METHOD=EXPERIMENTAL /STATISTICS=MCA. Widyo Pura Buana - MCA Struktur Data MCA dengan SPSS Widyo Pura Buana - MCA 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) Widyo Pura Buana - MCA MCAa N Predicted Mean Deviation Unadjusted Adjusted for Factors Unadjusted Adjusted 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 Deviation Mean Row Task Difficulty Easy 6 2 = 6 4 Row(i)-Grand Mean Difficult 2 -2 = 2 4 Column Arousal Low 2 -2 = 2 4 Column(j)-Grand Mean Medium 5 1 = 5 4 High 5 1 = 5 4 Grand Mean 4 Widyo Pura Buana - MCA Factor Summarya Eta Beta Formula Adjusted for Factors Performance Task Difficulty (Row) .577 .577 =SQRT( SSRow/ SSTotal ) =SQRT(120/360) Arousal (Column) .408 .408 =SQRT( SSColumn/ SSTotal ) =SQRT(60/360) Widyo Pura Buana - MCA Model Goodness of Fit R R Squared Performance by Task Difficulty, Arousal .707 .500 =SQRT(R-Squared) = SSModel/SSTotal Widyo Pura Buana - MCA Multiple Classification Analysis with Interaction Widyo Pura Buana - MCA Syntax SPSS MCA *MCA model with categorical predictors, interaction:. ANOVA Performance by Difficulty (1,2) Arousal (1,3) /MAXORDERS=ALL /METHOD=EXPERIMENTAL /STATISTICS=MCA. Widyo Pura Buana - 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 .008 2-Way Interactions Task Difficulty * Arousal 60.000 2 30.000 6.000 .008 Model 240.000 5 48.000 9.600 .000 Residual 120.000 24 5.000 Total 360.000 29 12.414 Widyo Pura Buana - MCA Graphical display of interactions Two ways to display previous results lo med hiArousal0.002.004.006.008.0010.00Mean ScoreDifficultydifficulteasyeasy difficultDifficulty0.002.004.006.008.0010.00Mean ScoreArousalhilomedWidyo Pura Buana - MCA MCA ~ GLM Factorial Anova Widyo Pura Buana - MCA MCA ~ GLM Factorial Anova MULTIPLE 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 Widyo Pura Buana - MCA 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 Widyo Pura Buana - MCA ( )( ) ijk i j k ijijY o | o| c = + + + +0 1 2Treatment A. : pH o o o = = =0 1 2Treatment B. : qH | | | = = =0 11 12Interaction. : pqH o| o| o| = = =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 Widyo Pura Buana - MCA Widyo Pura Buana - MCA Widyo Pura Buana - MCA Widyo Pura Buana - MCA Widyo Pura Buana - MCA Widyo Pura Buana - MCA