Logistic regression - Revision history

Michael: /* R example */

2024-03-03T05:59:20Z

R example

← Older revision		Revision as of 05:59, 3 March 2024
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	# Definite the logistic function		# Definite the logistic function
	~~# https://www.dataquest.io/blog/write-functions-in-r/~~
	logit <- function(t) {		logit <- function(t) {
	sigma=1/(1+exp(-t))		sigma=1/(1+exp(-t))
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	[1] Done calculation!		[1] Done calculation!
	</pre>		</pre>


	==See also==		==See also==

Michael: +R example

2024-03-03T03:51:20Z

+R example

← Older revision		Revision as of 03:51, 3 March 2024
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	ylabel('Probability of passing the exam (-)');		ylabel('Probability of passing the exam (-)');
	</pre>		</pre>

			==R example==
			<pre>
			noquote ("---------------------------------------------------------------------------------------------------")
			noquote ("A script in R to learn about logistic regression")
			noquote ("---------------------------------------------------------------------------------------------------")

			# Load library
			library(rms)

			# Data from example on 'Logistic regression' page of Wikipedia - https://en.wikipedia.org/wiki/Logistic_regression
			y=c( 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1 )
			x=c( 0.50, 0.75, 1.00, 1.25, 1.50, 1.75, 1.75, 2.00, 2.25, 2.50, 2.75, 3.00, 3.25, 3.50, 4.00, 4.25, 4.50, 4.75, 5.00, 5.50 )

			# Make dataframe
			mydata=data.frame(x,y)

			# Create logistic regression model
			mylrm=lrm(y~x, mydata)

			z=predict(mylrm)

			# Definite the logistic function
			# https://www.dataquest.io/blog/write-functions-in-r/
			logit <- function(t) {
			sigma=1/(1+exp(-t))
			return(sigma)
			}

			# Get p values from the z values
			logit(z)

			ypred=logit(z)

			# Get the coefficients from the LR model
			options(digits=20)
			coef(mylrm)

			# Calculating the p values using the equation
			beta0=-4.0777133660750397581
			beta1=1.5046454013690906404
			ycalc=1/(1+exp(-(beta0+beta1*x)))

			# Check the calculation
			noquote("The check...")
			ycalc-ypred

			# Add ycalc to dataframe
			mydata=data.frame(x,y,ypred)

			# Plot result
			plot(x,ypred, main="Probability of Passing versus Time Studied", ylab="Probability of Passing", xlab="Time Studied in Hours")

			# Show results
			options(digits=7)
			noquote("The model...")
			mylrm

			noquote("The input values and predicted values...")
			mydata

			noquote("Done calculation!")
			</pre>
			===Output===
			<pre>
			[1] ---------------------------------------------------------------------------------------------------
			[1] A script in R to learn about logistic regression
			[1] ---------------------------------------------------------------------------------------------------

			[1] The check...
			[1] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
			[1] The model...
			Logistic Regression Model

			lrm(formula = y ~ x, data = mydata)

			Model Likelihood Discrimination Rank Discrim.
			Ratio Test Indexes Indexes
			Obs 20 LR chi2 11.67 R2 0.589 C 0.895
			0 10 d.f. 1 R2(1,20) 0.413 Dxy 0.790
			1 10 Pr(> chi2) 0.0006 R2(1,15) 0.509 gamma 0.798
			max \|deriv\| 1e-07 Brier 0.137 tau-a 0.416

			Coef S.E. Wald Z Pr(>\|Z\|)
			Intercept -4.0777 1.7610 -2.32 0.0206
			x 1.5046 0.6287 2.39 0.0167

			[1] The input values and predicted values...
			x y ypred
			1 0.50 0 0.03471034
			2 0.75 0 0.04977295
			3 1.00 0 0.07089196
			4 1.25 0 0.10002862
			5 1.50 0 0.13934447
			6 1.75 0 0.19083651
			7 1.75 1 0.19083651
			8 2.00 0 0.25570318
			9 2.25 1 0.33353024
			10 2.50 0 0.42162653
			11 2.75 1 0.51501086
			12 3.00 0 0.60735864
			13 3.25 1 0.69261733
			14 3.50 0 0.76648083
			15 4.00 1 0.87444750
			16 4.25 1 0.91027764
			17 4.50 1 0.93662366
			18 4.75 1 0.95561071
			19 5.00 1 0.96909707
			20 5.50 1 0.98519444
			[1] Done calculation!
			</pre>


	==See also==		==See also==

Michael at 17:07, 8 April 2022

2022-04-08T17:07:51Z

← Older revision		Revision as of 17:07, 8 April 2022
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	===Ordered LR===		===Ordered LR===
	If the dependent variable is categorical and can be ordered in a meaningful way (e.g. ''Grade 1'', ''Grade 2'', ''Grade 3''), ''ordered logistic regression'' is used.<ref>Ordinal Logistic Regression \| R Data Analysis Examples. UCLA. URL: [https://stats.idre.ucla.edu/r/dae/ordinal-logistic-regression/ https://stats.idre.ucla.edu/r/dae/ordinal-logistic-regression/]. Accessed on: March 24, 2018</ref>		If the dependent variable is categorical and can be ordered in a meaningful way (e.g. ''Grade 1'', ''Grade 2'', ''Grade 3''), ''ordered logistic regression'' is used.<ref>Ordinal Logistic Regression \| R Data Analysis Examples. UCLA. URL: [https://stats.idre.ucla.edu/r/dae/ordinal-logistic-regression/ https://stats.idre.ucla.edu/r/dae/ordinal-logistic-regression/]. Accessed on: March 24, 2018</ref>

			==Convergence==
			If an individual predictor variable is ''not'' predictive (e.g. one pathologist never calls a diagnosis) the data has ''complete separation'' and will not converge.

	==GNU/Octave example==		==GNU/Octave example==

Michael: /* Ordered LR */ fix typo

2020-11-30T14:51:38Z

Ordered LR: fix typo

← Older revision		Revision as of 14:51, 30 November 2020
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	===Ordered LR===		===Ordered LR===
	If the dependent variable is categorical and can be ordered in a meaningful way (e.g. ''Grade 1'', ''Grade 2'', ''Grade 3''), ''ordered logistic ~~regrssion~~'' is used.<ref>Ordinal Logistic Regression \| R Data Analysis Examples. UCLA. URL: [https://stats.idre.ucla.edu/r/dae/ordinal-logistic-regression/ https://stats.idre.ucla.edu/r/dae/ordinal-logistic-regression/]. Accessed on: March 24, 2018</ref>		If the dependent variable is categorical and can be ordered in a meaningful way (e.g. ''Grade 1'', ''Grade 2'', ''Grade 3''), ''ordered logistic regression'' is used.<ref>Ordinal Logistic Regression \| R Data Analysis Examples. UCLA. URL: [https://stats.idre.ucla.edu/r/dae/ordinal-logistic-regression/ https://stats.idre.ucla.edu/r/dae/ordinal-logistic-regression/]. Accessed on: March 24, 2018</ref>

	==GNU/Octave example==		==GNU/Octave example==

Michael: /* Special types of LR */

2018-03-24T16:38:20Z

Special types of LR

← Older revision		Revision as of 16:38, 24 March 2018
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	'''Logistic regression''', abbreviated '''LR''', is a type of curve fitting. It used for categorical dependent (outcome) variables. Examples of categorical dependent variables are: (1) pass/fail, (2) dead/alive.		'''Logistic regression''', abbreviated '''LR''', is a type of curve fitting. It used for categorical dependent (outcome) variables. Examples of categorical dependent variables are: (1) pass/fail, (2) dead/alive.

	==~~Special types~~ of LR==		==Types of logistic regression==
	===Multinomial LR===		===Multinomial LR===
	If the dependent variable is categorical and the categories are mutually exclusive (e.g. ''benign'', ''suspicious'', ''malignant'', ''insufficient''), ''multinomial logistic regression'' is used.		If the dependent variable is categorical and the categories are mutually exclusive (e.g. ''benign'', ''suspicious'', ''malignant'', ''insufficient''), ''multinomial logistic regression'' is used.

Michael at 16:36, 24 March 2018

2018-03-24T16:36:26Z

← Older revision		Revision as of 16:36, 24 March 2018
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	'''Logistic regression''', abbreviated '''LR''', is a type of curve fitting. It used for categorical outcome variables. Examples of categorical ~~outcomes~~ variables are: (1) pass/fail, (2) dead/alive.		'''Logistic regression''', abbreviated '''LR''', is a type of curve fitting. It used for categorical dependent (outcome) variables. Examples of categorical dependent variables are: (1) pass/fail, (2) dead/alive.

	==Special types of LR==		==Special types of LR==

Michael at 16:33, 24 March 2018

2018-03-24T16:33:16Z

← Older revision		Revision as of 16:33, 24 March 2018
Line 1:		Line 1:
	'''Logistic regression''' is a type of curve fitting. It used for categorical outcome variables. Examples of categorical outcomes variables are: (1) pass/fail, (2) dead/alive.		'''Logistic regression''', abbreviated '''LR''', is a type of curve fitting. It used for categorical outcome variables. Examples of categorical outcomes variables are: (1) pass/fail, (2) dead/alive.

	==Special types of LR==		==Special types of LR==

Michael at 16:32, 24 March 2018

2018-03-24T16:32:06Z

← Older revision		Revision as of 16:32, 24 March 2018
Line 1:		Line 1:
	'''Logistic regression''' is a type of curve fitting. It used for ~~discrete~~ outcome variables~~, e.g~~. pass or fail.		'''Logistic regression''' is a type of curve fitting. It used for categorical outcome variables. Examples of categorical outcomes variables are: (1) pass/fail, (2) dead/alive.

	==Special types of LR==		==Special types of LR==
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	===Ordered LR===		===Ordered LR===
	If the dependent variable is categorical and ordered (e.g. ''Grade 1'', ''Grade 2'', ''Grade 3''), ''ordered logistic regrssion'' is used.<ref>Ordinal Logistic Regression \| R Data Analysis Examples. UCLA. URL: [https://stats.idre.ucla.edu/r/dae/ordinal-logistic-regression/ https://stats.idre.ucla.edu/r/dae/ordinal-logistic-regression/]. Accessed on: March 24, 2018</ref>		If the dependent variable is categorical and can be ordered in a meaningful way (e.g. ''Grade 1'', ''Grade 2'', ''Grade 3''), ''ordered logistic regrssion'' is used.<ref>Ordinal Logistic Regression \| R Data Analysis Examples. UCLA. URL: [https://stats.idre.ucla.edu/r/dae/ordinal-logistic-regression/ https://stats.idre.ucla.edu/r/dae/ordinal-logistic-regression/]. Accessed on: March 24, 2018</ref>

	==GNU/Octave example==		==GNU/Octave example==

Michael at 16:28, 24 March 2018

2018-03-24T16:28:46Z

← Older revision		Revision as of 16:28, 24 March 2018
Line 1:		Line 1:
	'''Logistic regression''' is a type of curve fitting. It used for discrete outcome variables, e.g. pass or fail.		'''Logistic regression''' is a type of curve fitting. It used for discrete outcome variables, e.g. pass or fail.

	If the dependent variable is categorical (e.g. ''~~tubular adenoma~~'', ''~~hyperplastic polyp~~''), ''multinomial logistic regression'' is used.		==Special types of LR==
			===Multinomial LR===
			If the dependent variable is categorical and the categories are mutually exclusive (e.g. ''benign'', ''suspicious'', ''malignant'', ''insufficient''), ''multinomial logistic regression'' is used.

			===Ordered LR===
			If the dependent variable is categorical and ordered (e.g. ''Grade 1'', ''Grade 2'', ''Grade 3''), ''ordered logistic regrssion'' is used.<ref>Ordinal Logistic Regression \| R Data Analysis Examples. UCLA. URL: [https://stats.idre.ucla.edu/r/dae/ordinal-logistic-regression/ https://stats.idre.ucla.edu/r/dae/ordinal-logistic-regression/]. Accessed on: March 24, 2018</ref>

	==GNU/Octave example==		==GNU/Octave example==
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	*[[Mathematics]].		*[[Mathematics]].
	*[[Statistics]].		*[[Statistics]].

			==References==
			{{Reflist\|1}}

	==External links==		==External links==

Michael: /* GNU/Octave example */ tweak

2017-03-21T12:16:45Z

GNU/Octave example: tweak

← Older revision		Revision as of 12:16, 21 March 2017
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	% [[ alpha se_alpha zvalue_alpha zvalue_alpha^2 P_Wald_alpha ]		% [[ alpha se_alpha zvalue_alpha zvalue_alpha^2 P_Wald_alpha ]
	% [ beta_1 se_beta_1 zvalue_beta_1 zvalue_beta_1^2 P_Wald_beta_1 ]		% [ beta_1 se_beta_1 zvalue_beta_1 zvalue_beta_1^2 P_Wald_beta_1 ]
	% [ beta_2 se_beta_2 zvalue_beta_2 ~~zvalue_beta_1~~^2 P_Wald_beta_2 ]		% [ beta_2 se_beta_2 zvalue_beta_2 zvalue_beta_2^2 P_Wald_beta_2 ]
	% [ ... ... ... ... ... ]		% [ ... ... ... ... ... ]
	% [ beta_n se_beta_n zvalue_beta_n ~~zvalue_beta_1~~^2 P_Wald_beta_n ]]		% [ beta_n se_beta_n zvalue_beta_n zvalue_beta_n^2 P_Wald_beta_n ]]
	logit_arr=zeros(size(beta,1)+1,5);		logit_arr=zeros(size(beta,1)+1,5);
	logit_arr(1,1)=theta;		logit_arr(1,1)=theta;