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poisson

Member Training: Logistic Regression for Count and Proportion Data

by Karen Grace-Martin Leave a Comment

Most of us know that binary logistic regression is appropriate when the outcome variable has two possible outcomes: success and failure.

There are two more situations that are also appropriate for binary logistic regression, but they don’t always look like they should be.

[Read more…] about Member Training: Logistic Regression for Count and Proportion Data

Tagged With: Bernoulli, binomial, Discrete Counts, logistic regression, normal distribution, outcome variable, poisson

Related Posts

  • Member Training: Making Sense of Statistical Distributions
  • Member Training: Explaining Logistic Regression Results to Non-Researchers
  • Member Training: Types of Regression Models and When to Use Them
  • Member Training: A Predictive Modeling Primer: Regression and Beyond

Poisson or Negative Binomial? Using Count Model Diagnostics to Select a Model

by Jeff Meyer 7 Comments

How do you choose between Poisson and negative binomial models for discrete count outcomes?

One key criterion is the relative value of the variance to the mean after accounting for the effect of the predictors. A previous article discussed the concept of a variance that is larger than the model assumes: overdispersion.

(Underdispersion is also possible, but much less common).

There are two ways to check for overdispersion: [Read more…] about Poisson or Negative Binomial? Using Count Model Diagnostics to Select a Model

Tagged With: count model, dispersion statistic, Model Fit, negative binomial, overdispersion, poisson, predicted count, residual plot

Related Posts

  • Overdispersion in Count Models: Fit the Model to the Data, Don’t Fit the Data to the Model
  • The Problem with Linear Regression for Count Data
  • The Importance of Including an Exposure Variable in Count Models
  • Analyzing Zero-Truncated Count Data: Length of Stay in the ICU for Flu Victims

Member Training: Making Sense of Statistical Distributions

by guest Leave a Comment

Many who work with statistics are already functionally familiar with the normal distribution, and maybe even the binomial distribution.

These common distributions are helpful in many applications, but what happens when they just don’t work?

This webinar will cover a number of statistical distributions, including the:

  • Poisson and negative binomial distributions (especially useful for count data)
  • Multinomial distribution (for responses with more than two categories)
  • Beta distribution (for continuous percentages)
  • Gamma distribution (for right-skewed continuous data)
  • Bernoulli and binomial distributions (for probabilities and proportions)
  • And more!

We’ll also explore the relationships among statistical distributions, including those you may already use, like the normal, t, chi-squared, and F distributions.


Note: This training is an exclusive benefit to members of the Statistically Speaking Membership Program and part of the Stat’s Amore Trainings Series. Each Stat’s Amore Training is approximately 90 minutes long.

[Read more…] about Member Training: Making Sense of Statistical Distributions

Tagged With: Bernoulli, beta, binomial, distributions, gamma, Multinomial, negative binomial, poisson, statistical distributions

Related Posts

  • Member Training: Logistic Regression for Count and Proportion Data
  • Poisson or Negative Binomial? Using Count Model Diagnostics to Select a Model
  • Analyzing Zero-Truncated Count Data: Length of Stay in the ICU for Flu Victims
  • Overdispersion in Count Models: Fit the Model to the Data, Don’t Fit the Data to the Model

Analyzing Zero-Truncated Count Data: Length of Stay in the ICU for Flu Victims

by Jeff Meyer 3 Comments

by Jeff Meyer

It’s that time of year: flu season.

Let’s imagine you have been asked to determine the factors that will help a hospital determine the length of stay in the intensive care unit (ICU) once a patient is admitted.

The hospital tells you that once the patient is admitted to the ICU, he or she has a day count of one. As soon as they spend 24 hours plus 1 minute, they have stayed an additional day.

Clearly this is count data. There are no fractions, only whole numbers.

To help us explore this analysis, let’s look at real data from the State of Illinois. We know the patients’ ages, gender, race and type of hospital (state vs. private).

A partial frequency distribution looks like this: [Read more…] about Analyzing Zero-Truncated Count Data: Length of Stay in the ICU for Flu Victims

Tagged With: Count data, linear regression, negative binomial, poisson, predictors, Truncated

Related Posts

  • The Problem with Linear Regression for Count Data
  • The Importance of Including an Exposure Variable in Count Models
  • Poisson or Negative Binomial? Using Count Model Diagnostics to Select a Model
  • Getting Accurate Predicted Counts When There Are No Zeros in the Data

Two-Way Tables and Count Models: Expected and Predicted Counts

by Jeff Meyer Leave a Comment

by Jeff Meyer

In a previous article, we discussed how incidence rate ratios calculated in a Poisson regression can be determined from a two-way table of categorical variables.

Statistical software can also calculate the expected (aka predicted) count for each group. Below is the actual and expected count of the number of boys and girls participating and not participating in organized sports.

cm-twowaytables-1

 

 

 

 

 

 

 

The value in the top of each cell is the actual count (40 boys do not play organized sports) and the bottom value is the expected/predicted count (36 boys are predicted to not play organized sports).

The Poisson model that we ran in the previous article generated the following table: [Read more…] about Two-Way Tables and Count Models: Expected and Predicted Counts

Tagged With: categorical variable, expected count, poisson, predicted count, two-way table

Related Posts

  • Poisson or Negative Binomial? Using Count Model Diagnostics to Select a Model
  • Getting Accurate Predicted Counts When There Are No Zeros in the Data
  • The Problem with Linear Regression for Count Data
  • Analyzing Zero-Truncated Count Data: Length of Stay in the ICU for Flu Victims

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

by Jeff Meyer Leave a Comment

by Jeff Meyer

If you have count data you use a Poisson model for the 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. A survey was done in Australia during the peak of the flu season. The outcome variable is the total number of times people asked for medical advice from any source over a two-week period.

We are trying to determine what influences people with flu symptoms to seek medical advice. The mean number of times was 0.516 times and the variance 1.79.

The mean does not equal the variance even after accounting for the model’s predictors.

Here are the results for this model: [Read more…] about Overdispersion in Count Models: Fit the Model to the Data, Don’t Fit the Data to the Model

Tagged With: count model, negative binomial, overdispersion, poisson

Related Posts

  • Poisson or Negative Binomial? Using Count Model Diagnostics to Select a Model
  • The Importance of Including an Exposure Variable in Count Models
  • The Problem with Linear Regression for Count Data
  • Analyzing Zero-Truncated Count Data: Length of Stay in the ICU for Flu Victims

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This Month’s Statistically Speaking Live Training

  • February Member Training: Choosing the Best Statistical Analysis

Upcoming Workshops

  • Logistic Regression for Binary, Ordinal, and Multinomial Outcomes (May 2021)
  • Introduction to Generalized Linear Mixed Models (May 2021)

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