StatLab Articles

Multinomial logit models allow us to model membership in a group based on known variables. For example, the operating system preferences of a university’s students could be classified as “Windows,” “Mac,” or “Linux.” Perhaps we would like to better understand why students choose one OS versus another. We might want to build a statistical model that allows us to predict the probability of selecting an OS based on information such as sex, major, financial aid, and so on. Multinomial logit modeling allows us to propose and fit such models.

What are empirical cumulative distribution functions and what can we do with them? To answer the first question, let’s first step back and make sure we understand "distributions", or more specifically, "probability distributions".

A Basic Probability Distribution

Imagine a simple event, say flipping a coin 3 times. Here are all the possible outcomes, where H = head and T = tails:

Let’s say we’re interested in modeling the number of auto accidents that occur at various intersections within a city. Upon collecting data after a certain period of time, perhaps we notice two intersections have the same number of accidents, say 25. Is it correct to conclude these two intersections are similar in their propensity for auto accidents?

Regular expressions (or regex) are tools for matching patterns in character strings. These can be useful for finding words or letter patterns in text, parsing filenames for specific information, and interpreting input formatted in a variety of ways (e.g., phone numbers). The syntax of regular expressions is generally recognized across operating systems and programming languages. Although this tutorial will use R for examples, most of the same regex could be used in unix commands or in Python.

Shiny is an R package that facilitates the creation of interactive web apps using R code, which can be hosted locally, on the shinyapps server, or on your own server. Shiny apps can range from extremely simple to incredibly sophisticated. They can be written purely with R code or supplemented with HTML, CSS, or JavaScript. Visit R studio’s shiny gallery to view some examples.

As data scientists, we’re often most excited about the final layer of analysis. Once all the data are cleaned and stored in a format readable by our favorite programming language (Python, R, STATA, etc.), the most fun part of our work is when we’re finding counter-intuitive causations with statistical methods. If you can prove that the mutual presence of McDonalds really does prevent wars between countries or that an increase in diversity really does boost business profitability, that is a good day.

One of the basic assumptions of linear modeling is constant, or homogeneous, variance. What does that mean exactly? Let’s simulate some data that satisfies this condition to illustrate the concept.

Below we create a sorted vector of numbers ranging from 1 to 10 called x, and then create a vector of numbers called y that is a function of x. When we plot x vs y, we get a straight line with an intercept of 1.2 and a slope of 2.1.

When you import or load data into R, the data are stored in random-access memory (RAM). This is the memory that is deleted when you close R or shut off your computer. It’s very fast but temporary. If you save your data, it is saved to your hard drive. But when you open R again and load the data, once again it is loaded into RAM. While many newer computers come with lots of RAM (such as 16 GB), it’s not an infinite amount. When you open RStudio, you’re using RAM even if no data is loaded. Open a web browser or any other program and they too are loaded into RAM.

A count model is a linear model where the dependent variable is a count. For example, the number of times a car breaks down, the number of rats in a litter, the number of times a young student gets out of his seat, etc. Counts are either 0 or a positive whole number, which means we need to use special distributions to generate the data.

Logistic regression is a method for modeling binary data as a function of other variables. For example we might want to model the occurrence or non-occurrence of a disease given predictors such as age, race, weight, etc. The result is a model that returns a predicted probability of occurrence (or non-occurrence, depending on how we set up our data) given certain values of our predictors. We might also be able to interpret the coefficients in our model to summarize how a change in one predictor affects the odds of occurrence.