Datasets for Statistical Analysis: Generalized Linear Models

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Generalized Linear Models

• Logistic (binomial) regression
• Regression for counts (Poisson, log-linear models, negative binomial)
• Gamma regression
• Inverse Gaussian regression
• Tweedie regression
• Dispersion models (not strictly a glms)

Logistic (binomial) regression

• Noisy miner abundance
  The presence/absence of noisy miners
• AFL Football Department spending and results
  Spending of AFL clubs compared to performance
• Vasco-constriction reflex after deep breaths
  Binary data with two associated predictors
• Occurrence of lizards
  Binary data of the presence/absence of lizards
• Rodent captures in California
  The number of rodents species captured (out of six considered)
• Participation of women in the paid workforce
  The proportion of women in the paid workforce in 1975, with seven possible predictors
• Loss of consciousness in pilots
  Binary data: Whether pilots shows signs of black-out
• Potency of three poisons
  The number of insects killed at various doses of three poisons
• Toowoomba household survey
  The outcome of successive visits to households in Toowoomba to complete a survey
• Rolling dice
  The probability of rolling a six with various kinds of non-cubic dice were estimated.
• Neuralgia data
  A small example of a binary response.
• Age of menarche in Polish girls
  A useful, small example.
• Insecticide doses and tobacco budworm
• Insecticide doses and insects
  Three insecticides at various doses
• Pilot deaths
  The data show a significant trend in deaths with increasing age.
• Fissures in turbine wheels
  The number (proportion) of turbines failing after a number of hours of use.
• Toxoplasmosis and rainfall
The proportion of people sampled in 34 cities in El Salvador who tested positive for toxoplasmosis. A polynomial relationship.
• British election candidates
  The number of female and male candidates running for office at the 1992 British general elections
• What to do with the inheritance?
  A study on whether the inheritance should be kept in the family, or be spent
• Deaths from preventable diseases
  The number of deaths from preventable diseases in Australia

Regression for counts (Poisson, log-linear models, negative binomial)

• Skin cancers in women
  The number of skin cancers in women in two area of the USA
• Species richness for ants
  The species richness for ants (number of ant species)
• Noisy miner abundance
  The abundance of noisy miners
• Spider density
  Density of certain spiders
• Apprentice migration to Edinburgh
  The number of apprentices moving to Edinburgh from other Scottish counties
• Demand for public transit services in rural areas
  Two small data sets for regression, with a number of potential predictors
• Counting snow geese
  The number of snow geese estimated by two observers, compared to an accurate count from a photo. The data show a linear relationship.
• Mutagenicity assay
  A Poisson glm with a non-standard predictor and repeated measurements
• South African Birth to Ten study
  An example of Simpson's paradox: mothers classified by race, group, and whether they had medical aid
• Treatment of kidney stones
  An example of Simpson's paradox: success rates of two treatment methods classified by size of the stones
• Food poisoning
  Data from an outbreak of food poisoning
• Rootstock data
  Survival of plum rootstocks; a three-way table of counts
• Tonsils and pyogenes
  The number of carriers and non-carriers of pyogenes related to tonsil size
• Tumours and Avadex
  The incidence of tumours in mice exposed to Avadex
• Third Party Motor Insurance in Sweden
  For this data, the number of claims has a Poisson distribution.
• Coronary heart disease, smoking and coffee intake
• Fathers' and Son's occupations (506)
• Depression and children
  This data includes a zero cell.
• Accidents on Danish highways
• Depression in learning disabled and emotionally disturbed adolescents
  A four level contingency table classifying adolescents by age, gender, depression levels and whether they are seriously emotionally disturbed or learning disabled.
• Canadian cancer deaths
  A small, three factor contingency table with structural zeros.
• Gender differences in mathematics
  A three factor contingency table with one ordered factor.
• Equipment failures
  An example of a Poisson glm with an identity link function.
• Attitudes of Australians to genetically modified foods
  A small 2x2 contingency tables with no fixed margins.
• Smoking and survival of Whickham women
  A small contingency table with two other factors. An example of Simpson's Paradox.
• Danish lung cancer
  A Poisson rate problem
• Hospital length-of-stay for asthmatic children
  Count data without zeros (truncated Poisson)
• Strip searched, but no charges laid
  The number of people strip-searched, and the number of those released without charges laid.

Gamma regression

• Elastomer viscosity
  A designed experiment measuring the viscosity of elastomers as a function of oil and filler
• Third Party Motor Insurance in Sweden
  For this data, the amount of each claim follows a gamma distribution very nicely.
• Two assay experiments for a hormone
  A small, simple example of a gamma glm with an identity link function.
• Leukaemia survival times
  A small, simple example of a gamma glm. The original source (pre-glms days) uses an exponential distribution with identity link, though an inverse link appears more sensible.
• Stopping distance
  A dataset with two variables, an increasing variance and a quadratic relationship.
• Wheat yields
  A small dataset with different responses to planting density with potential outliers.
• Nambeware products
  The time taken to polish and grind numerous products made by Nambe Mills.
• Height and resting pulse
  The heights and resting pulses for a sample of hospital patients. The link function is probably the identity.
• Cell mutant frequencies in children
  The somatic cell mutant frequencies at the hrpt locus of the X-chormosome in healthy children
• Lung weight of mice
  The lung weight of two types of mice at various ages
• Magazine revenue
  The revenue from magazine based on pages of advertising; non-constant variance and outliers
• Dialectric breakdown strength
  Performance degradation data from accelerated tests; can be modelled with a log-normal or gamma distribution, or with a Tweedie distribution with p about 1.8
• Oxidation rate of benzene
  Modelled well with a gamma glm using a reciprocal of oxygen concetration and a log-link

Inverse Gaussian regression

• Height and pulse rate
  The relationship is not very strong.
• the datsets from Folks, JL and Chhikara, RS (1978). `The inverse Gaussian distribution and its statistical application---a review' in Journal of the Royal Statistical Society, Series B, 40(3), 263--289.

Tweedie distributions

• Participation of women in the paid workforce
  The number of paid hours of work perhaps follows a Tweedie distribution (data contains exact zeros)
• Fine root dataset
  An example of a Tweedie distribution with index between 1 and 2.
• Daily average wind speeds in Ireland (windpseeds.dat)
  A large data set (6574 by 15), and an example of a Tweedie distribution with index between 1 and 2.
• Survival time of animals
  The mle estimate of p is about 3.85.
• Third Party Motor Insurance in Sweden
  For this data, the number of claims has a Poisson distribution, and the amount of each claim follows a gamma distribution very nicely. The total claim has a Tweedie distribution.
• January snowfall in inches recorded at Seattle from 1906 to 1960
  The mle estimate of p is about 1.52.
• Number of cyclamen flowers
  For this data, the mle estimate of p is about 2.5.
• Daily rainfall, Melbourne, Australia from 1981 to 1990.
  For example, April total rainfall can be modelled with a Tweedie distribution with p=1.58.
• Butterfat and dairy cattle
  This data can be modelled with a Tweedie distribution with p of about 5.
• Cosmetic company use of polythene
  This data can be modelled with a Tweedie distribution with p between 1 and 2
• Dialectric breakdown strength
  Performance degradation data from accelerated tests; can be modelled with a log-normal or gamma distribution, or with a Tweedie distribution with p about 1.8

See also

• R programs for evaluating Tweedie distributions
• R programs for fitting Tweedie generalized linear models

The following datasets from Hand et al. may also lend themselves to a Tweedie generalized linear model:

• Survival time of leukaemia patients (424)
• Survival times of animals (403) (the classic data set from Box and Cox, introducing the Box-Cox transformation). A Tweedie model with p=3.85 seems appropriate. Also available as poison.dat.

Dispersion models

• Wind directions at Gorleston
  This data can be modelled using a von Mises (or von Mises-Fisher) distribution, a dispersion model but not an EDM.
• Distance and direction travelled by blue periwinkles
  An example of a dispersion model