「Regression model」の版間の差分

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&dagger;'Multivariable' can be rephrased as 'Multiple'; Multivariable is <font color="red">'''NOT equal to 'Multivariate'!!'''</font>
 
&dagger;'Multivariable' can be rephrased as 'Multiple'; Multivariable is <font color="red">'''NOT equal to 'Multivariate'!!'''</font>
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===How to convert coefficient of binary logistic regressoin to odds ratio===
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About a binary logistic regression formula
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:<math>
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\log Y = \log \frac{p}{1-p} = a + b_1X_1 + b_2X_2 + b_3X_3 + \cdots
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</math>
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<math>
 +
\begin{array}{lcl}
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\log Y & = & a + b_1X_1 + b_2X_2 + b_3X_3 + \cdots \\
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\log \frac{p}{1-p} & = & a + b_1X_1 + b_2X_2 + b_3X_3 + \cdots \\
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\end{array}
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</math>
  
 
==Generalized linear model==
 
==Generalized linear model==

2023年2月4日 (土) 17:32時点における版

Basics & Definition
Epidemiology
Odds in statistics and Odds in a horse race
Collider bias
Data distribution
Statistical test
Regression model
Multivariate analysis
Marginal effects
Prediction and decision
Table-related commands in STATA
Missing data and imputation

Classification of Regression models

Independent variable (exposure)
Univariable (single variable) Multivariable (multiple variables) How to derive coefficients [math]\displaystyle{ b_i }[/math]
Dependent
variable
(outcome)
Continuous
  • Single linear regression
[math]\displaystyle{ Y = a + bX }[/math]
  • Multivariable† linear regression
[math]\displaystyle{ Y = a + b_1X_1 + b_2X_2 + b_3X_3 + \cdots }[/math]

Least squares method

Binary
  • Single binary logistic regression
[math]\displaystyle{ \log Y = a + bX }[/math]
where [math]\displaystyle{ Y }[/math] is odds of outcome [math]\displaystyle{ \frac{p}{1-p} }[/math]
  • Multivariable† binary logistic regression
[math]\displaystyle{ \log Y = a + b_1X_1 + b_2X_2 + b_3X_3 + \cdots }[/math]
where [math]\displaystyle{ Y }[/math] is odds of outcome [math]\displaystyle{ \frac{p}{1-p} }[/math]

Maximum likelihood estimation method

Multinominal
≥ 3
  • Single multinominal logistic regression
  • Multivariable† multinominal logistic regression

Maximum likelihood estimation method

Ordinal
  • Single ordinal logistic regression
  • Multivariable† ordinal logistic regression

Maximum likelihood estimation method

Rate ratio
  • Multivariable Poisson regression
[math]\displaystyle{ \log Y = a + b_1X_1 + b_2X_2 + b_3X_3 + \cdots }[/math]
where [math]\displaystyle{ Y }[/math] is rate ratio [math]\displaystyle{ \frac{events_1/person \text{-} time_1}{events_2/person \text{-} time_2} }[/math]

Maximum likelihood estimation method

Survival time
  • Multivariable proportional hazard regression
    = Cox hazard regression
[math]\displaystyle{ \log h(T) = \log h_0(T) + b_1X_1 + b_2X_2 + b_3X_3 + \cdots }[/math]
where [math]\displaystyle{ h(T) }[/math] is the hazard at time [math]\displaystyle{ T }[/math]
and [math]\displaystyle{ h_0(T) }[/math] is the baseline hazard at time [math]\displaystyle{ T }[/math]

Maximum likelihood estimation method

†'Multivariable' can be rephrased as 'Multiple'; Multivariable is NOT equal to 'Multivariate'!!

How to convert coefficient of binary logistic regressoin to odds ratio

About a binary logistic regression formula

[math]\displaystyle{ \log Y = \log \frac{p}{1-p} = a + b_1X_1 + b_2X_2 + b_3X_3 + \cdots }[/math]

[math]\displaystyle{ \begin{array}{lcl} \log Y & = & a + b_1X_1 + b_2X_2 + b_3X_3 + \cdots \\ \log \frac{p}{1-p} & = & a + b_1X_1 + b_2X_2 + b_3X_3 + \cdots \\ \end{array} }[/math]

Generalized linear model

Penalized multivariable logistic regression model

Restricted cubic spline