logistic regression with the continuous predictor

The LOGISTIC Procedure

Model Information
Data Set WORK.MYDATA
Response Variable outcome
Number of Response Levels 2
Model binary logit
Optimization Technique Fisher's scoring

Number of Observations Read 124
Number of Observations Used 118

Response Profile
Ordered
Value		 outcome Total
Frequency
1 no 70
2 yes 48

Probability modeled is outcome='no'.



Note: 6 observations were deleted due to missing values for the response or explanatory variables.

Model Convergence Status
Convergence criterion (GCONV=1E-8) satisfied.

Model Fit Statistics
Criterion Intercept
Only		 Intercept
and
Covariates
AIC 161.457 116.384
SC 164.228 121.925
-2 Log L 159.457 112.384

R-Square 0.3290 Max-rescaled R-Square 0.4439

Testing Global Null Hypothesis: BETA=0
Test Chi-Square DF Pr > ChiSq
Likelihood Ratio 47.0730 1 <.0001
Score 26.1402 1 <.0001
Wald 20.1538 1 <.0001

Analysis of Maximum Likelihood Estimates
Parameter DF Estimate Standard
Error		 Wald
Chi-Square		 Pr > ChiSq
Intercept 1 2.1943 0.4180 27.5625 <.0001
predictor 1 -0.0362 0.00806 20.1538 <.0001

Odds Ratio Estimates
Effect Point Estimate 95% Wald
Confidence Limits
predictor 0.964 0.949 0.980

Association of Predicted Probabilities and
Observed Responses
Percent Concordant 84.4 Somers' D 0.689
Percent Discordant 15.5 Gamma 0.689
Percent Tied 0.1 Tau-a 0.335
Pairs 3360 c 0.844

Wald Confidence Interval for Parameters
Parameter Estimate 95% Confidence Limits
Intercept 2.1943 1.3751 3.0135
predictor -0.0362 -0.0520 -0.0204

Profile Likelihood Confidence Interval for Odds Ratios
Effect Unit Estimate 95% Confidence Limits
predictor 1.0000 0.964 0.948 0.978

ROC Curve for Model


logistic regression with the continuous predictor

Obs id predictor_cutoff
1 33 48.3


logistic regression using the cutoff of the predictor

The LOGISTIC Procedure

Model Information
Data Set WORK.MYDATA
Response Variable outcome
Number of Response Levels 2
Model binary logit
Optimization Technique Fisher's scoring

Number of Observations Read 124
Number of Observations Used 118

Response Profile
Ordered
Value		 outcome Total
Frequency
1 no 70
2 yes 48

Probability modeled is outcome='yes'.



Note: 6 observations were deleted due to missing values for the response or explanatory variables.

Class Level Information
Class Value Design
Variables
PredictNumcut 0 1
  1 -1

Model Convergence Status
Convergence criterion (GCONV=1E-8) satisfied.

Model Fit Statistics
Criterion Intercept
Only		 Intercept
and
Covariates
AIC 161.457 117.051
SC 164.228 122.592
-2 Log L 159.457 113.051

Testing Global Null Hypothesis: BETA=0
Test Chi-Square DF Pr > ChiSq
Likelihood Ratio 46.4062 1 <.0001
Score 44.1278 1 <.0001
Wald 36.6758 1 <.0001

Type 3 Analysis of Effects
Effect DF Wald
Chi-Square		 Pr > ChiSq
PredictNumcut 1 36.6758 <.0001

Analysis of Maximum Likelihood Estimates
Parameter   DF Estimate Standard
Error		 Wald
Chi-Square		 Pr > ChiSq
Intercept   1 -0.1642 0.2386 0.4735 0.4914
PredictNumcut 0 1 -1.4451 0.2386 36.6758 <.0001

Odds Ratio Estimates
Effect Point Estimate 95% Wald
Confidence Limits
PredictNumcut 0 vs 1 0.056 0.022 0.142

Association of Predicted Probabilities and
Observed Responses
Percent Concordant 64.3 Somers' D 0.607
Percent Discordant 3.6 Gamma 0.895
Percent Tied 32.1 Tau-a 0.296
Pairs 3360 c 0.804