1 / 8

Modeling Ordinal Associations Bin Hu

Modeling Ordinal Associations Bin Hu. Linear-by-Linear Association in two-way table Modeling Fitting The “Sex Opinion” Example Directed Ordinal Test of Independence. For two-way case, two ordinal variables assign the order score for row score and the column scores are and

Télécharger la présentation

Modeling Ordinal Associations Bin Hu

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Modeling Ordinal AssociationsBin Hu • Linear-by-Linear Association in two-way table • Modeling Fitting • The “Sex Opinion” Example • Directed Ordinal Test of Independence

  2. For two-way case, two ordinal variables assign the order score for row score and the column scores are and The model is with constrains Linear-by-Linear Association

  3. L-by-L model: A model for ordinal variables uses association terms that permit trends. In this model, there are 1+(I-1)+(J-1)+1=I+J parameters and only one parameter describing the association. The residual DF: IJ-I-J; beta>0, positive trend; beta<0, negative trend; otherwise, independent association. Obviously, when the data display a positive or negative trend, the L*L model fits better than the independence model.

  4. The result of MLE for L-by-L model is: Since the marginal distributions and hence marginal means and variances are identical for fitted and observed distributions, the third equation implied the correlation between the scores for X and Y is the same for both distributions. Since ui and vj are fixed, the L-by-L model has only one more parameter than independence model.

  5. Parameter Estimates ‘Sex Opinion’ in LL model Standard Wald 95% Confidence Chi- Parameter DF Estimate Error Limits Square Pr > ChiSq Intercept 1 0.4735 0.4339 -0.3769 1.3239 1.19 0.2751 premar 1 1 1.7537 0.2343 1.2944 2.2129 56.01 <.0001 premar 2 1 0.1077 0.1988 -0.2820 0.4974 0.29 0.5880 premar 3 1 -0.0163 0.1264 -0.2641 0.2314 0.02 0.8972 premar 4 0 0.0000 0.0000 0.0000 0.0000 . . birth 1 1 1.8797 0.2491 1.3914 2.3679 56.94 <.0001 birth 2 1 1.4156 0.1996 1.0243 1.8068 50.29 <.0001 birth 3 1 1.1551 0.1291 0.9021 1.4082 80.07 <.0001 birth 4 0 0.0000 0.0000 0.0000 0.0000 . . linlin 1 0.2858 0.0282 0.2305 0.3412 102.46 <.0001 Exp(0.4735+1.7537+1.8797+0.2858*1*1)=80.9 Exp(0.4735+0.1077+1.4156+0.2858*2*2)=23.1

  6. Birth Control Premarital SexSDI DI AG SAI Always Wrong 81 (42.4) 68 (51.2) 60 (86.4) 38 (67) (7.6) (80.9) (3.1) (67.6) (-4.1) (69.4) (-4.8) (29.1) Almost Wrong 24 (16) 26 (19.3) 29 (32.5) 14 (25.2) (2.3) (20.8) (1.8) (23.1) (-.8) (31.5) (-2.8) (17.6) Wrong Sometimes 18 (30.1) 41(36.3) 74 (61.2) 42 (47.4) (-2.7) (24.4) (1) (36.1) (2.2) (65.7) (-1) (48.8) Not Wrong 36(70.6) 57(85.2) 161(143.8) 157(111.4) (-6.1) (33) (-4.6) (65.1) (2.4) (157.4) (6.8) (155.5) a(b)(c)(d): a: observed count; b: independence model fit; the Pearson residuals for independence model fit; Linear-by-linear association model fit.

  7. Criteria For Assessing Goodness Of Fit For LL model Criterion DF Value Value/DF Deviance 8 11.5337 1.4417 Scaled Deviance 8 11.5337 1.4417 Pearson Chi-Square 8 11.5085 1.4386 Scaled Pearson X2 8 11.5085 1.4386 Log Likelihood 3041.7446 For Indept. Model Deviance 9 127.6529 14.1837 Scaled Deviance 9 127.6529 14.1837 Pearson Chi-Square 9 128.6836 14.2982 Scaled Pearson X2 9 128.6836 14.2982 Log Likelihood 2983.6850

  8. Independence Test :   Independence, ie. Beta=0 The likelihood-ratio test statistic is = 127.6-11.5 = 116.1 With df=1, P<0.0001, there is strong evidence of association. As for df, df of =1 is smaller than df of =(I-1)(J-1), the former is more powerful in testing the independence.

More Related