Differences Between the Normal and Poisson Distributions

The normal distribution is so ubiquitous in statistics that those of us who use a lot of statistics tend to forget it’s not always so common in actual data. And since the normal distribution is continuous, many people describe all numerical variables as continuous. I get it: I’m guilty of using those terms interchangeably, too, but they’re not exactly the same. Numerical variables can be either continuous or discrete. The difference? Continuous variables can take any number within a range. Discrete variables can only be whole numbers.

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Overdispersion in Count Models: Fit the Model to the Data, Don’t Fit the Data to the Model

If you have count data we use a Poisson model for our analysis, right? The key criterion for using a Poisson model is after accounting for the effect of predictors, the mean must equal the variance. If the mean doesn’t equal the variance then all we have to do is transform the data or tweak the model, correct? Let’s see how we can do this with some real data.

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The Impact of Removing the Constant from a Regression Model: The Categorical Case

In a simple linear regression model how the constant (aka, intercept) is interpreted depends upon the type of predictor (independent) variable.

If the predictor is categorical and dummy-coded, the constant is the mean value of the outcome variable for the reference category only. If the predictor variable is continuous, the constant equals the predicted value of the outcome variable when the predictor variable equals zero.

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Count Models: Understanding the Log Link Function

When we perform a statistical model, we are in a sense creating a mathematical equation. We have two parts to the equation. The left side of the equation is the sum of that fixed component and the random component. The random component has a probability distribution. Since the outcome variable includes that random component, it too follows a probability distribution. On the right side of the equation is a link function, which is the link between the mean of Y and the structural component. It’s very possible you have run models without being aware of this. Some software packages have predictor models (e.g., Stata’s Poisson and nbreg) which use a default link function. But if you run a generalized linear model (GLM), then you must select the link function that fits your random components.

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December 2016 Member Webinar: A Gentle Introduction to Generalized Linear Mixed Models – Part 2

Generalized linear mixed models (GLMMs) are incredibly useful tools for working with complex, multi-layered data. But they can be tough to master. In this follow-up to October’s webinar (“A Gentle Introduction to Generalized Linear Mixed Models – Part 1”), you’ll learn the major issues involved in working with GLMMs and how to incorporate these models into your own work.

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The Difference Between Truncated and Censored Data

There are two types of bounded data that have direct implications for how to work with them in analysis: censored and truncated data. Understanding the difference is a critical first step when undertaking a statistical analysis.

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Principal Component Analysis for Ordinal Scale Items

Principal Component Analysis is really, really useful. You use it to create a single index variable from a set of correlated variables. In fact, the very first step in Principal Component Analysis is to create a correlation matrix (a.k.a., a table of bivariate correlations). The rest of the analysis is based on this correlation matrix. You don’t usually see this step — it happens behind the scenes in your software. Most PCA procedures calculate that first step using only one type of correlations: Pearson. And that can be a problem. Pearson correlations assume all variables are normally distributed. That means they have to be truly quantitative, symmetric, and bell shaped. And unfortunately, many of the variables that we need PCA for aren’t. Likert Scale items are a big one.

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Outliers and Their Origins

Outliers are one of those realities of data analysis that no one can avoid. Those pesky extreme values cause biased parameter estimates, non-normality in otherwise beautifully normal variables, and inflated variances. Everyone agrees that outliers cause trouble with parametric analyses. But not everyone agrees that they’re always a problem, or what to do about them even if they are. Sometimes a nonparametric or robust alternative is available–and sometimes not. There are a number of approaches in statistical analysis for dealing with outliers and the problems they create.

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November 2016 Member Webinar: The LASSO Regression Model

The LASSO model (Least Absolute Shrinkage and Selection Operator) is a recent development that allows you to find a good fitting model in the regression context. It avoids many of the problems of overfitting that plague other model-building approaches. In this month’s Statistically Speaking webinar, guest instructor Steve Simon, PhD, will explain what overfitting is — and why it’s a problem.

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Two Types of Effect Size Statistic: Standardized and Unstandardized

Effect size statistics are all the rage these days. Journal editors are demanding them. Committees won’t pass dissertations without them. But the reason to compute them is not just that someone wants them — they can truly help you understand your data analysis.

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