 # GLM - GAM

ROC Curves in Two Lines of R Code. By Bob Horton, Microsoft Data Scientist ROC curves are commonly used to characterize the sensitivity/specificity tradeoffs for a binary classifier. Most machine learning classifiers produce real-valued scores that correspond with the strength of the prediction that a given case is positive. Turning these real-valued scores into yes or no predictions requires setting a threshold; cases with scores above the threshold are classified as positive, and cases with scores below the threshold are predicted to be negative. Different threshold values give different levels of sensitivity and specificity. A high threshold is more conservative about labelling a case as positive; this makes it less likely to produce false positive results but more likely to miss cases that are in fact positive (lower rate of true positives).

The calculation has two steps: Logistic Regression Tutorial for Machine Learning. Logistic regression is one of the most popular machine learning algorithms for binary classification. This is because it is a simple algorithm that performs very well on a wide range of problems. In this post you are going to discover the logistic regression algorithm for binary classification, step-by-step. After reading this post you will know: How to calculate the logistic function.How to learn the coefficients for a logistic regression model using stochastic gradient descent.How to make predictions using a logistic regression model. This post was written for developers and does not assume a background in statistics or probability. Let’s get started. Logistic Regression for Machine Learning. Logistic regression is another technique borrowed by machine learning from the field of statistics. It is the go-to method for binary classification problems (problems with two class values). In this post you will discover the logistic regression algorithm for machine learning. After reading this post you will know: The many names and terms used when describing logistic regression (like log odds and logit).The representation used for a logistic regression model.Techniques used to learn the coefficients of a logistic regression model from data.How to actually make predictions using a learned logistic regression model.Where to go for more information if you want to dig a little deeper. This post was written for developers interested in applied machine learning, specifically predictive modeling. Logistic Regression with R - Listen Data. #Read Data File mydata <- read.csv(" #Summary summary(mydata) #Cross Tab xtabs(~admit + rank, data = mydata) How to use Multinomial and Ordinal Logistic Regression in R ? Introduction Most of us have limited knowledge of regression. Of which, linear and logistic regression are our favorite ones. As an interesting fact, regression has extended capabilities to deal with different types of variables. Do you know, regression has provisions for dealing with multi-level dependent variables too? I’m sure, you didn’t. For multi-level dependent variables, there are many machine learning algorithms which can do the job for you; such as naive bayes, decision tree, random forest etc. In this article, I’ve explained the method of using multinomial and ordinal regression. Prediction Intervals for Poisson Regression. Different from the confidence interval that is to address the uncertainty related to the conditional mean, the prediction interval is to accommodate the additional uncertainty associated with prediction errors. As a result, the prediction interval is always wider than the confidence interval in a regression model. In the context of risk modeling, the prediction interval is often used to address the potential model risk due to aforementioned uncertainties. While calculating prediction interval of OLS regression based on the Gaussian distributional assumption is relatively straightforward with the off-shelf solution in R, it could be more complicated in a Generalized Linear Model, e.g.

Poisson regression. In this post, I am going to show two empirical methods, one based on bootstrapping and the other based on simulation, calculating the prediction interval of a Poisson regression. The first method shown below is based on the bootstrapping with following steps: 1. 2. InformationValue - r-statistics.co. The functions in InformationValue package are broadly divided in following categories: 1. Diagnostics of predicted probability scores 2. Simple Guide to Logistic Regression in R. Introduction Every machine learning algorithm works best under a given set of conditions. Making sure your algorithm fits the assumptions / requirements ensures superior performance. You can’t use any algorithm in any condition. For example: Have you ever tried using linear regression on a categorical dependent variable? Don’t even try! Instead, in such situations, you should try using algorithms such as Logistic Regression, Decision Trees, SVM, Random Forest etc. Data Perspective: Introduction to Logistic Regression with R. In my previous blog I have explained about linear regression. In today’s post I will explain about logistic regression. Consider a scenario where we need to predict a medical condition of a patient (HBP) ,HAVE HIGH BP or NO HIGH BP, based on some observed symptoms – Age, weight, Issmoking, Systolic value, Diastolic value, RACE, etc.. In this scenario we have to build a model which takes the above mentioned symptoms as input values and HBP as response variable. Note that the response variable (HBP) is a value among a fixed set of classes, HAVE HIGH BP or NO HIGH BP.

How to perform a Logistic Regression in R. Logistic regression is a method for fitting a regression curve, y = f(x), when y is a categorical variable. The typical use of this model is predicting y given a set of predictors x. The predictors can be continuous, categorical or a mix of both. The categorical variable y, in general, can assume different values. In the simplest case scenario y is binary meaning that it can assume either the value 1 or 0. Logistic Regression in R – Part Two. My previous post covered the basics of logistic regression. We must now examine the model to understand how well it fits the data and generalizes to other observations. The evaluation process involves the assessment of three distinct areas – goodness of fit, tests of individual predictors, and validation of predicted values – in order to produce the most useful model.

While the following content isn’t exhaustive, it should provide a compact ‘cheat sheet’ and guide for the modeling process. Evaluating Logistic Regression Models in R. This post provides an overview of performing diagnostic and performance evaluation on logistic regression models in R. After training a statistical model, it’s important to understand how well that model did in regards to it’s accuracy and predictive power. The following content will provide the background and theory to ensure that the right technique are being utilized for evaluating logistic regression models in R. Logistic Regression Example We will use the GermanCredit dataset in the caret package for this example.

It contains 62 characteristics and 1000 observations, with a target variable (Class) that is allready defined. Logistic Regression Fundamentals « GormAnalysis. Logistic regression is a generalized linear model most commonly used for classifying binary data. It’s output is a continuous range of values between 0 and 1 (commonly representing the probability of some event occurring), and it’s input can be a multitude of real-valued and discrete predictors. Motivation Suppose you want to predict the probability someone is a homeowner based solely on their age. You might have a dataset like As with any binary variable, it makes sense to code True values as 1s and False values as 0s.

There’s definitely more positive samples as age increases which makes sense. Evaluating Logistic Regression Models. Logistic regression is a technique that is well suited for examining the relationship between a categorical response variable and one or more categorical or continuous predictor variables. The model is generally presented in the following format, where β refers to the parameters and x represents the independent variables. log(odds)=β0+β1∗x1+... +βn∗xn The log(odds), or log-odds ratio, is defined by ln[p/(1−p)] and expresses the natural logarithm of the ratio between the probability that an event will occur, p(Y=1), to the probability that it will not occur.

We are usually concerned with the predicted probability of an event occuring and that is defined by p=1/1+exp^−z, where z=β0+β1∗x1+... Logistic regression. Problem. Visualising theoretical distributions of GLMs. Two weeks ago I discussed various linear and generalised linear models in R using ice cream sales statistics. The data showed not surprisingly that more ice cream was sold at higher temperatures. icecream <- data.frame( temp=c(11.9, 14.2, 15.2, 16.4, 17.2, 18.1, 18.5, 19.4, 22.1, 22.6, 23.4, 25.1), units=c(185L, 215L, 332L, 325L, 408L, 421L, 406L, 412L, 522L, 445L, 544L, 614L) )

Generalised Linear Models in R. Linear models are the bread and butter of statistics, but there is a lot more to it than taking a ruler and drawing a line through a couple of points. Some time ago Rasmus Bååth published an insightful blog article about how such models could be described from a distribution centric point of view, instead of the classic error terms convention. I think the distribution centric view makes generalised linear models (GLM) much easier to understand as well. That’s the purpose of this post. Using data on ice cream sales statistics I will set out to illustrate different models, starting with traditional linear least square regression, moving on to a linear model, a log-transformed linear model and then on to generalised linear models, namely a Poisson (log) GLM and Binomial (logistic) GLM.

More on Prediction From Log-Linear Regressions. My therapy sessions are actually going quite well. I'm down to just one meeting with Jane a week, now. Yes, there are still far too many log-linear regressions being bandied around, but I'm learning to cope with it! Example 2014.7: Simulate logistic regression with an interaction.

## GAM

Regression - Assumptions of generalised linear model. Some R Resources for GLMs. R Data Analysis Examples: Logit Regression. R - Generalized linear Models. Glm for predicting rates. I often need to build a predictive model that estimates rates. The example of our age is: ad click through rates (how often a viewer clicks on an ad estimated as a function of the features of the ad and the viewer). » Poisson regression fitted by glm(), maximum likelihood, and MCMC. The goal of this post is to demonstrate how a simple statistical model (Poisson log-linear regression) can be fitted using three different approaches.

I want to demonstrate that both frequentists and Bayesians use the same models, and that it is the fitting procedure and the inference that differs. ROC curves and classification. To get back to a question asked after the last course (still on non-life insurance), I will spend some time to discuss ROC curve construction, and interpretation. Consider the dataset we’ve been using last week, Dave Giles' Blog: Forecasting From Log-Linear Regressions. I was in (yet another) session with my analyst, "Jane", the other day, and quite unintentionally the conversation turned, once again, to the subject of "semi-log" regression equations. After my previous rant to discussion with her about this matter, I've tried to stay on the straight and narrow.

It's better for my blood pressure, apart from anything else! Anyway, somehow how we got back this topic, and she urged me to get some related issues off my chest. This is therapy, after all! Right at the outset, let me state quite categorically that lots of people estimate semi-logarithmic regressions for the wrong reasons. I mean, we wouldn't use an inconsistent estimator, would we? R Data Analysis Examples: Logit Regression. FAQ: How do I interpret odds ratios in logistic regression? R - Generalized linear Models. Logistic regression and categorical covariates.