Category:Fitting logistic regression models - Revision history

Bosmana fem: Bosmana fem moved page Fitting logistic regression models to Category:Fitting logistic regression models

2023-03-25T20:23:43Z

Bosmana fem moved page Fitting logistic regression models to Category:Fitting logistic regression models

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Bosmana fem at 19:34, 25 March 2023

2023-03-25T19:34:49Z

← Older revision		Revision as of 19:34, 25 March 2023
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	The log-likelihood is defined as:		The log-likelihood is defined as:
	[[File:3060.image015.gif-550x0.png\|~~800px~~\|frameless\|center]]		[[File:3060.image015.gif-550x0.png\|1000px\|frameless\|center]]

	In which		In which
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	Computations from deviances		Computations from deviances
	[[File:4188.LRS.gif-550x0.png\|~~600px~~\|frameless\|center]]		[[File:4188.LRS.gif-550x0.png\|800px\|frameless\|center]]

	In which D- and D+ are, respectively, the deviances of the models without and with the variable of interest.		In which D- and D+ are, respectively, the deviances of the models without and with the variable of interest.
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			==FEM PAGE CONTRIBUTORS 2007==
			; Editor
			: Fernando Simon
			; Original Author
			: Alain Moren
			; Contributors
			: Arnold Bosman
			: Lisa Lazareck
			: Fernando Simon

	[[Category:Logistic Regression]]		[[Category:Logistic Regression]]

Bosmana fem at 19:33, 25 March 2023

2023-03-25T19:33:21Z

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	The Likelihood ratio statistic (LRS) can be directly computed from the likelihood functions of both models.		The Likelihood ratio statistic (LRS) can be directly computed from the likelihood functions of both models.
			[[File:0447.image023.gif-550x0.png\|600px\|frameless\|center]]

	Probabilities are always less than one, so log-likelihoods are always negative; we then work with negative log-likelihoods for convenience.		Probabilities are always less than one, so log-likelihoods are always negative; we then work with negative log-likelihoods for convenience.
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	The LRS does not tell us if a particular independent variable is more important than others. This can be done, however, by comparing the likelihood of the overall model with a reduced model, which drops one of the independent variables.		The LRS does not tell us if a particular independent variable is more important than others. This can be done, however, by comparing the likelihood of the overall model with a reduced model, which drops one of the independent variables.

	In that case, the LRS tests if the logistic regression coefficient for the dropped variable equals 0. If so it would justify dropping the variable from the model. A non-significant LRS indicates no difference between the full and the reduced models.		In that case, the LRS tests if the logistic regression coefficient for the dropped variable equals 0. If so it would justify dropping the variable from the model. A non-significant LRS indicates no difference between the full and the reduced models.

	Alternatively, LRS can be computed from deviances.		Alternatively, LRS can be computed from deviances.

	Computations from deviances		Computations from deviances
			[[File:4188.LRS.gif-550x0.png\|600px\|frameless\|center]]

			In which D- and D+ are, respectively, the deviances of the models without and with the variable of interest.

	In which D- and D+ are, respectively the deviances of the models without and with the variable of interest.

	The deviance can be computed as follows:		The deviance can be computed as follows:
			[[File:3252.D-.gif-550x0.png\|800px\|frameless\|center]]

			[[File:3301.D+.gif-550x0.png\|800px\|frameless\|center]]



	(A saturated model is a model in which there are as many parameters as data points.)		(A saturated model is a model in which there are as many parameters as data points.)



	Under the hypothesis that β1= 0, LRS follows a chi-square distribution with 1 degree of freedom. The derived p-value can be computed.		Under the hypothesis that β1= 0, LRS follows a chi-square distribution with 1 degree of freedom. The derived p-value can be computed.

	The following table illustrates the result of the analysis (using a logistic regression package) of a study assessing risk factors for myocardial infarction. The LRS equals 138,7821 (p < 0,001) suggesting that oral contraceptive (OC) use is a significant predictor of the outcome.		The following table illustrates the result of the analysis (using a logistic regression package) of a study assessing risk factors for myocardial infarction. The LRS equals 138,7821 (p < 0,001), suggesting that oral contraceptive (OC) use is a significant predictor of the outcome.

	Table 1: Risk factors for myocardial infarction. ~~Logistic~~ regression model including a single independent variable (OC)		Table 1: Risk factors for myocardial infarction. A logistic regression model including a single independent variable (OC)

	{\| class="wikitable" style="background-color:#FFF;"		{\| class="wikitable" style="background-color:#FFF;"

Bosmana fem at 19:26, 25 March 2023

2023-03-25T19:26:43Z

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	Table 1: Risk factors for myocardial infarction. Logistic regression model including a single independent variable (OC)		Table 1: Risk factors for myocardial infarction. Logistic regression model including a single independent variable (OC)

	Number of valid Observations		{\| class="wikitable" style="background-color:#FFF;"
			\|-
	449		! colspan="2" \| Number of valid Observations
			! 449
			!
			!
			! colspan="2" \|
			\|-
			\| colspan="2" \| Model Fit Results
			\| Value
	Model Fit Results		\| DF
			\| p-value
	Value		\| colspan="2" \|
			\|-
	DF		\| colspan="2" \| Likelihood ratio statistic
			\| style="background-color:#FF9;" \| 138,7821
	p-value		\| 2
			\| < 0.001
			\| colspan="2" \|
			\|}
	Likelihood ratio statistic

	138,7821

	2

	< 0.001



	~~Parameter Estimates~~

			Parameter Estimates --------------------------------------------------------- 95% C.I.
	{\| class="wikitable" style="text-align:right; vertical-align:bottom;"		{\| class="wikitable" style="text-align:right; vertical-align:bottom;"
	\|-		\|-
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	\|}		\|}

	Parameter Estimates ------------------------------------------ 5% C.I.		Parameter Estimates --------------------------------------------------------- 95% C.I.

	{\| class="wikitable" style="background-color:#FFF;"		{\| class="wikitable" style="background-color:#FFF;"

Bosmana fem at 19:25, 25 March 2023

2023-03-25T19:25:09Z

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	Parameter Estimates 95% C.I.		Parameter Estimates ------------------------------------------ 5% C.I.

	{\| class="wikitable" style="background-color:#FFF;"		{\| class="wikitable" style="background-color:#FFF;"

Bosmana fem at 19:24, 25 March 2023

2023-03-25T19:24:25Z

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	\|		\|
	\|		\|
	\|-
	~~\| colspan="2" \| Parameter Estimates~~
	\|
	\|
	\|
	~~\| colspan="2" \| 95% C.I.~~
	\|}		\|}

			Parameter Estimates 95% C.I.

	{\| class="wikitable" style="background-color:#FFF;"		{\| class="wikitable" style="background-color:#FFF;"

Bosmana fem at 19:22, 25 March 2023

2023-03-25T19:22:51Z

← Older revision		Revision as of 19:22, 25 March 2023
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	Table 2: Risk factors for myocardial infarction. Logistic regression model including two independent variable (OC and AGE)		Table 2: Risk factors for myocardial infarction. Logistic regression model including two independent variable (OC and AGE)

	Number of valid Observations		{\| class="wikitable" style="background-color:#FFF;"
			\|-
	449		! colspan="2" \| Number of valid Observations
			! 449
			!
			!
			!
			!
			\|-
			\| colspan="2" \| Model Fit Results
			\| Value
			\| DF
	Model Fit Results		\| p-value
			\|
	Value		\|
			\|-
	DF		\| colspan="2" \| Likelihood ratio statistic
			\| style="background-color:#FF9;" \| 16,7253
	p-value		\| 1
			\| < 0.001
			\|
			\|
			\|-
			\| colspan="2" \| Parameter Estimates
	Likelihood ratio statistic		\|
			\|
	16,7253		\|
			\| colspan="2" \| 95% C.I.
	1		\|}

	< 0.001





	~~Parameter Estimates~~

Bosmana fem at 19:21, 25 March 2023

2023-03-25T19:21:01Z

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Bosmana fem at 19:08, 25 March 2023

2023-03-25T19:08:58Z

← Older revision		Revision as of 19:08, 25 March 2023
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	The log-likelihood is defined as:		The log-likelihood is defined as:
			[[File:3060.image015.gif-550x0.png\|600px\|frameless\|center]]


	In which		In which

	<!-~~-[endif~~]~~-->~~		[[File:5074.probY.gif-550x0.png\|600px\|frameless\|center]]

Bosmana fem at 19:04, 25 March 2023

2023-03-25T19:04:59Z

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