Results

Logistic Regression

Model Summary - Scored
Model		Deviance		AIC		BIC		df		ΔΧ²		p		McFadden R²		Nagelkerke R²		Tjur R²		Cox & Snell R²
M₀		510.630		512.630		517.396		867						0.000				0.000
M₁		415.338		423.338		442.403		864		95.292		< .001		0.187		0.234		0.157		0.104

Note. M₁ includes Ability, Position, Ability:Position

Coefficients
												Wald Test						95% Confidence interval (odds ratio scale)
Model				Estimate		Robust Standard Error		Odds Ratio		z		Wald Statistic		df		p		Lower bound		Upper bound
M₀		(Intercept)		2.358		0.121		10.573		19.521		381.089		1		< .001		8.344		13.398
M₁		(Intercept)		1.786		1.193		5.967		1.497		2.058		1		0.134		0.576		61.827
		Ability		0.084		0.186		1.088		0.453		0.192		1		0.651		0.756		1.566
		Position		-1.176		0.377		0.309		-3.120		10.057		1		0.002		0.147		0.646
		Ability * Position		0.191		0.062		1.210		3.060		10.003		1		0.002		1.071		1.368

Note. Scored level 'Scored penalty' coded as class 1.

Multicollinearity Diagnostics
		Tolerance		VIF
Ability		0.168		5.964
Position		0.065		15.418
Ability:Position		0.064		15.734

Influential Cases
Case Number		Std. Residual		Scored		Predicted Value		Residual		Cook's Distance
.		.		.		.		.		.

Note. No influential cases found.

Performance Diagnostics

Confusion matrix
		Predicted
Observed		Missed penalty		Scored penalty		% Correct
Missed penalty		10		65		13.333
Scored penalty		5		788		99.369
Overall % Correct						91.935

Note. The cut-off value is set to 0.5

Diagnostic plots

Independent - predicted plots

Ability

Position

Ability ✻ Position

Position ✻ Ability

Logistic Regression: Factor

Model Summary - Scored
Model		Deviance		AIC		BIC		df		ΔΧ²		p		McFadden R²		Nagelkerke R²		Tjur R²		Cox & Snell R²
M₀		510.630		512.630		517.396		867						0.000				0.000
M₁		422.624		434.624		463.221		862		88.006		< .001		0.172		0.217		0.135		0.096
M₂		422.624		434.624		463.221		862		0.000				0.172		0.217		0.135		0.096

Note. M₁ includes Position, Ability
Note. M₂ includes Position, Ability

Coefficients
												Wald Test
Model				Estimate		Standard Error		Odds Ratio		z		Wald Statistic		df		p
M₀		(Intercept)		2.358		0.121		10.573		19.521		381.089		1		< .001
M₁		(Intercept)		-1.510		0.578		0.221		-2.613		6.826		1		0.009
		Position (2)		-0.732		0.455		0.481		-1.609		2.589		1		0.108
		Position (3)		-0.302		0.466		0.739		-0.647		0.419		1		0.517
		Position (4)		-0.273		0.453		0.761		-0.603		0.364		1		0.547
		Position (5)		-0.582		0.450		0.559		-1.293		1.671		1		0.196
		Ability		0.673		0.079		1.960		8.520		72.585		1		< .001
M₂		(Intercept)		-1.510		0.578		0.221		-2.613		6.826		1		0.009
		Position (2)		-0.732		0.455		0.481		-1.609		2.589		1		0.108
		Position (3)		-0.302		0.466		0.739		-0.647		0.419		1		0.517
		Position (4)		-0.273		0.453		0.761		-0.603		0.364		1		0.547
		Position (5)		-0.582		0.450		0.559		-1.293		1.671		1		0.196
		Ability		0.673		0.079		1.960		8.520		72.585		1		< .001

Note. Scored level 'Scored penalty' coded as class 1.

Performance Diagnostics

Confusion matrix
		Predicted
Observed		Missed penalty		Scored penalty		% Correct
Missed penalty		3		72		4.000
Scored penalty		6		787		99.243
Overall % Correct						91.014

Note. The cut-off value is set to 0.5

Logistic Regression: Linearity

Model Summary - Scored
Model		Deviance		AIC		BIC		df		ΔΧ²		p		McFadden R²		Nagelkerke R²		Tjur R²		Cox & Snell R²
M₀		510.630		512.630		517.396		867						0.000				0.000
M₁		424.875		434.875		458.705		863		85.755		< .001		0.168		0.212		0.131		0.094
M₂		421.841		435.841		469.204		861		3.034		0.219		0.174		0.219		0.138		0.097

Note. M₁ includes Ability, Position, Ln_Ability, Ln_Position
Note. M₂ includes Ability, Position, Ln_Ability, Ln_Position, Ability:Ln_Ability, Position:Ln_Position

Coefficients
										Wald Test
Model				Estimate		Standard Error		z		Wald Statistic		df		p
M₀		(Intercept)		2.358		0.121		19.521		381.089		1		< .001
M₁		(Intercept)		-0.946		1.408		-0.672		0.452		1		0.501
		Ability		0.927		0.409		2.268		5.145		1		0.023
		Position		0.215		0.412		0.523		0.273		1		0.601
		Ln_Ability		-1.391		2.104		-0.661		0.437		1		0.509
		Ln_Position		-0.713		1.053		-0.677		0.458		1		0.498
M₂		(Intercept)		-20.588		11.343		-1.815		3.295		1		0.070
		Ability		8.673		10.135		0.856		0.732		1		0.392
		Position		14.758		9.839		1.500		2.250		1		0.134
		Ln_Ability		-11.412		13.637		-0.837		0.700		1		0.403
		Ln_Position		-12.463		7.982		-1.561		2.438		1		0.118
		Ability * Ln_Ability		-2.158		2.800		-0.771		0.594		1		0.441
		Position * Ln_Position		-4.916		3.329		-1.477		2.182		1		0.140

Note. Scored level 'Scored penalty' coded as class 1.

Logistic Collinearity

Model Summary - Scored
Model		Deviance		AIC		BIC		df		ΔΧ²		p		McFadden R²		Nagelkerke R²		Tjur R²		Cox & Snell R²
M₀		510.630		512.630		517.396		867						0.000				0.000
M₁		425.738		431.738		446.036		865		84.892		< .001		0.166		0.210		0.132		0.093

Note. M₁ includes Ability, Position

Coefficients
												Wald Test
Model				Estimate		Standard Error		Odds Ratio		z		Wald Statistic		df		p
M₀		(Intercept)		2.358		0.121		10.573		19.521		381.089		1		< .001
M₁		(Intercept)		-1.687		0.555		0.185		-3.040		9.244		1		0.002
		Ability		0.665		0.078		1.945		8.547		73.051		1		< .001
		Position		-0.056		0.094		0.946		-0.589		0.347		1		0.556

Note. Scored level 'Scored penalty' coded as class 1.

Multicollinearity Diagnostics
		Tolerance		VIF
Ability		1.000		1.000
Position		1.000		1.000

Performance Diagnostics

Confusion matrix
		Predicted
Observed		Missed penalty		Scored penalty		% Correct
Missed penalty		1		74		1.333
Scored penalty		3		790		99.622
Overall % Correct						91.129

Note. The cut-off value is set to 0.5