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CRITERION-RELATED VALIDITY – PREDICTIVE

CRITERION-RELATED VALIDITY – PREDICTIVE. LECTURE 10 EPSY 625. EMPIRICAL METHODS FOR VALIDITY. Predictive validity logistic regression discriminant analysis/cluster analysis correlation/structural equation modeling Concurrent validity correlation/structural equation modeling

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CRITERION-RELATED VALIDITY – PREDICTIVE

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  1. CRITERION-RELATED VALIDITY – PREDICTIVE LECTURE 10 EPSY 625

  2. EMPIRICAL METHODS FOR VALIDITY • Predictive validity • logistic regression • discriminant analysis/cluster analysis • correlation/structural equation modeling • Concurrent validity • correlation/structural equation modeling • factor analysis • Construct validity • factor analysis • multitrait-multimethod analysis

  3. PREDICTIVE VALIDITY- logistic regression Binary group: (0,1) such as hired vs. not hired, general vs. clinical Transform binary score into logit: L(y) = log[p/(1-p)] Predict L(y) = b1 x, where x is a test score Can use SPSS LOGISTIC option in REGRESSION analysis

  4. VARIABLE LABELS t1 ANXIETY t2 ATTITUDE TO PARENTS t3 ATTITUDE TO SCHOOL t4 ATTITUDE TO TEACHER t5 ATYPICALITY t6 DEPRESSION t7 INTERPERSONAL RELATIONS t8 SENSE OF INADEQUACY t9 LOCUS OF CONTROL t10 SELF ESTEEM t11 SELF RELIANCE t12 SENSATION SEEKING t13 SOMATICIZATION t14 SOCIAL STRESS

  5. Multinomial regression • Extension of logistic regression • 3 or more groups contrasted • Ordered groups- compute “threshhold for classification as a “1” or “2” , “2” or “3” etc • Unordered groups- can do pairwise logistic regression or a priori contrasts among groups as the organizer for binomial contrasting (eg. groups A and B vs. groups C, D, and E)

  6. PREDICTIVE VALIDITY – DISCRIMINANT ANALYSIS Group membership Test scores eg, which MMPI scales differentiate/separate/predict manic depressives from normal functioning adults? This will be useful upon intake or commitment hearings in addition to clinical judgement

  7. DISCRIMINANT ANALYSIS • 2 Groups: statistical procedure is identical to multiple regression with group (1 or 2) as dependent variable, k test scores as predictors • 3 or more Groups: discriminant analysis separates the groups based on a weighted sum of the predictors in standardized form

  8. 2 Group Analysis • Model: y = b1x1 + b2x2 + …bkxk + b0 y = 1 or 2 (or any two discrete numbers) creates single predicted score Dhat which is the predicted score for each person. Can compare this predicted score with actual diagnoses or condition to determine % hit rate

  9. 2 Group Analysis y2 D=b1y1+b2y2 Group 1 means y1 R2 = SSD / SStot Group 2 means

  10. 2 Group hit rate Example: predict male (1) vs. female (2) differences based on interests x1, x2, … xk Each person receives a score yhat ; if yhat is below 1.5 the person is predicted to be a male, if over 1.5, a female. Out of 100 persons (50 M, 50 F), by chance we would classify 50 correctly by chance;

  11. 2 Group hit rate Cohen’s kappa will provide evidence for correct classification beyond chance: k = Pc - P0/[1 - P0] Alternatively, R2 for the regression provides evidence for classification beyond chance.

  12. Example: Gender predicted from music preferences R2 = SSb / SStot = .291/344.7 = .001

  13. Discriminant Analysis Wilks lambda = 1-R2

  14. males females w 0.0

  15. 3 Group discriminant analysis • 2 or more discriminant functions possible • # functions = min (#predictors, #gps-1) • Evaluate greatest function (group separation) first, each function successively • Examine joint classification for all significant functions

  16. 3 Group Analysis1st discriminant function Group 1 means y2 y1 Group 3 means Group 2 means Maximize SS between groups D1=b1y1+b2y2

  17. 3 Group Analysis2nd discriminant function Group 1 means y2 y1 Group 3 means Group 2 means D2=b3y1+b4y2 D1=b1y1+b2y2

  18. 3 Group Analysis Group 1 means R12 = SSD1 / SStot y2 D1=b1y1+b2y2 y1 Group 3 means Group 2 means D2=b3y1+b4y2 R22 = SSD2 / SStot

  19. 3 Group Analysis Group 1 means Discriminant function coefficients y2 y1 Group 3 means Group 2 means D2=b3y1+b4y2 D1=b1y1+b2y2

  20. Example: Ethnic music prefs

  21. Territorial Map Function 2 -3.0 -2.0 -1.0 .0 1.0 2.0 3.0 +---------+---------+---------+---------+---------+---------+ 3.0 + 21 + I 21 I I 21 I I 21 I I 21 I I 21 I 2.0 + 21 + + + + + + I 21 I I 21 I I 21 I I 21 I I 21 I 1.0 + 21 + + + + + + I 21 I I 21 I I 21 I I 21 * I I 21 I .0 + 21 + + * +* + + + I 21 I I 21 I I 21 I I 21 I I 21 I -1.0 + 21 + + + + + + I 21 I I 21 I I 21 I I 21 I I 21 I -2.0 + 21 + + + + + + I 21 I I 21 I I 21 I I 21 I I 21 I -3.0 + 21 + +---------+---------+---------+---------+---------+---------+ -3.0 -2.0 -1.0 .0 1.0 2.0 3.0 Canonical Discriminant Function 1 Symbol Group Label ------ ----- -------------------- 1 1 white 2 2 black 3 3 other * Indicates a group centroid

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