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Pythonで学ぶ一般化線形モデル

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更新日 2022/10

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コース説明

応答変数が二値・カウント・おおよそ正規分布といった異なるタイプでも、ひとつの枠組みで扱えるとしたらどうでしょうか。実は、それが現実に可能です。本コース「Generalized Linear Models in Python」では、ロジスティック回帰とPoisson回帰を学び、モデルの当てはめ方、理解の仕方、性能評価、そして新しいデータへの予測までを身につけます。世界最大規模の集団中毒事例、ヒラツメガニの営巣、ニューヨーク市の橋の自転車通行量カウントなど、実世界の研究データを使って実践します。

前提条件

Introduction to Linear Modeling in Python

1

Introduction to GLMs

Review linear models and learn how GLMs are an extension of the linear model given different types of response variables. You will also learn the building blocks of GLMs and the technical process of fitting a GLM in Python.

Going beyond linear regression

Applying linear models

Linear model, a special case of GLM

How to build a GLM?

Data type and distribution family

Linear model and a binary response variable

Comparing predicted values

How to fit a GLM in Python?

Model fitting step-by-step

Results of the model fit using summary()

Extracting parameter estimates

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2

Modeling Binary Data

This chapter focuses on logistic regression. You'll learn about the structure of binary data, the logit link function, model fitting, as well as how to interpret model coefficients, model inference, and how to assess model performance.

Binary data and logistic regression

Compute odds and probabilities

Fit logistic regression

Interpreting coefficients

Coefficients in terms of odds

Model formula

Interpreting logistic model

Rate of change in probability

Interpreting model inference

Statistical significance

Computing Wald statistic

Confidence intervals

Computing and describing predictions

Visualize model fit using regplot()

Compute predictions

Compute confusion matrix

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3

Modeling Count Data

Here you'll learn about Poisson regression, including the discussion on count data, Poisson distribution and the interpretation of the model fit. You'll also learn how to overcome problems with overdispersion. Finally, you'll get hands-on experience with the process of model visualization.

Count data and Poisson distribution

Visualize the response

Fitting a Poisson regression

Interpreting model fit

Estimate parameter lambda

Interpret Poisson coefficients

Poisson confidence intervals

The Problem of Overdispersion

Is the mean equal to the variance?

Computing expected number of counts

Checking for overdispersion

Fitting negative binomial

Confidence intervals for negative Binomial model

Plotting a regression model

Plotting data and linear model fit

Plotting fitted values

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4

Multivariable Logistic Regression

In this final chapter you'll learn how to increase the complexity of your model by adding more than one explanatory variable. You'll practice with the problem of multicollinearity, and with treating categorical and interaction terms in your model.

Multivariable logistic regression

Fit a multivariable logistic regression

The effect of multicollinearity

Compute VIF

Comparing models

Checking model fit

Compare two models

Deviance and linear transformation

Model formula

Model matrix for continuous variables

Variable transformation

Coding categorical variables

Categorical and interaction terms

Modeling with categorical variable

Interaction terms

Congratulations!

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Pythonで学ぶ一般化線形モデル

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