Question

Fit an initial model with the above covariates and examine the Odds ratios with their CI and comment on the results (as far as the OR are concerned).

Probability modeled is Pain-Yes Odds Ratios with 95% Wald Connderbc. Limits Treatment Dvs Duraton Odds Ratio Parttion for the Hosmer and Lemeshow Test Pain No Group Total ObservedExpected Observed Expected 5.90 5.78 5.49 4.91 4. 18 3.46 2.68 1.56 0.90 0.14 0.10 0.22 0.51 .09 1.82 2.54 3.32 4.44 5.10 5.86 5 5 6 7 6 5 6 10 6 5 Hosmer and Leme show Goodne ssof-Fit Test DF 8 Chi-square Pr> Chisq 8.4981 0.3864 Number of Observations Read 60 Number of Observations Used 60 Response Profile Total Value Pain Frequency 25 35 Ordered 1 Yes 2 No Probability modeled is Pain-Yes. Class Level Information Class Value Design Variables Treatment A Sex Model Convergence Status Convergence criterion (GCONV-1E-8) satisfied Analysis of Maximum Likel ihood E stmates Wald Error Chi-Square Pr>Chi Sq 5.5828 9.8049 Standard DFE mate Parameter Intercept Treatment A-3.1817 TreatmentB3.7085140 Sex Age Duration 0.0181 0.0017 0.0011 0.0214 0.0069 0 8591 -15.57446.5915 1.0161 10.5700 F 11.8322 0.7963 1 0.26210.0970 1-0.005860.0330 5 2946 7 2977 00315 Association of Predicted Proba bil ities and Observed Responses Percent Concordant 90.5 SomersD 0810 Percent Discordant 9.5 Gamma0.810 Percent Tied 0.0 Taua 0.401 Pairs 875 c 0.905 Odds Ra ธ° E sti mates and Wald Confidence Intervals Effect Trea tment A vSP 1.0000 Trea tment 8 vSP 1.0000 Sex F vs M Age Dura ธ0n Unit Estimate 95% Conf dence Limits 0.304 0.229 0.762 1.572 1.061 0.042 0.025 0.160 .300 0.994 0.006 0.003 0.034 075 0.932 10000 Model Fit Statistics Intercept and Criterion Intercept Only Covariates AIC SC 2 Log L 83.503 85.598 81.503 60.736 73.302 48.736 Testing Global Null Hypothesis: BETA-0 Test Likelihood Ratio Score Wald Chi-Square DF Pr> ChiSq 0001 0.0001 0.0130 32 7675 5 25.66665 4.45125 Type 3 Analysis of Effects Wald Effect Treatment2 Sex Age Duration1 DF Chi-Square Pr> ChiSq 0.0019 0.0214 0.0069 0.8591 12.5310 5.2946 7 2977 0.0315

Answer 1

Model F Statistics Intercept and Criterion Intercept Only Covaristes AIC Sc 2 Logt 3503 5 590 1 503 フ 302 Model fit statistics are Goodness of fit measures to compare one model with other. Lower these values the higher the desired model. The model with the intercept and predictor variables is better because its values are lower than intercept only model.

Testing Global Null Hypothel BETA- Test Likelihood Ratio 3276756 0001 Score Wald C Square OFPY Chis 564660 0001 44512 130 Testing if any of the estimated parameters significantly different than beta-0. All these three probabilities are less than 0.05%, so we reject null hypothesis and interpret that there is atleast of the independent variables with the coefficient not equal to 0.

Tye 3 Analysis of Efects Wald Treatme21253 Sen Age Duration 2946 72977 0315 Each and every individual parameter is statistically significant and different from 0. Coefficients of treatment, sex and age are significant beacuse its corresponding p values are less than 0.05. But the independent variable duration is insignificant with p value more than 0.05

2912 oces Provides a breakdown of the parameter estimates with the p-values. For those beta values are statistiscally significant with the p <0.05. The p>0.05 values of the parameters show thein coefficient is statistically not significant with beta-0. here with the coefficients of the parameter we can build a logistic regression model.

Logistic regression equation In (estimated odds ratio)-bn't bl.Χ, +62.X,+ b3.x,tb4.x, In (estimated_odds_ratio)-15.5766-3.1047.1-3.7005.2-1.0322.3+0.2427.4 06 0900 Every unit change in A changes the P by 0.042 times keeping sex, age, and duration constant. 95% confidence does not include 1 means that the odds ratio is statistically significant. The same thing is with Treatment B vs P and Sex F vs M,age. But the age and durations odds ratio are not significant because the interval includes 1.