Analysis of Categorical Data by Linear Models
Bibliographic Data
| ID | 23385341 |
|---|---|
| Authors | James E Grizzle, C F Starmer (0000-0002-9877-1537), Gary G Koch |
| Year | 1969 |
| Volume | 25 |
| Issue | 3 |
| Pages | 489 |
| Publication date | 1969-09-01 |
| Peer Reviewed | Yes |
| Open Access | No |
| Type | ARTICLE |
| Venue | Biometrics (JOURNAL) |
| Journal identifiers | ISSN: 0006-341X • E-ISSN: 1541-0420 |
| Publisher | JSTOR (PUBLISHER) |
| DOI | 10.2307/2528901 |
| PMID | 5824401 |
| OpenAlex | W2063803293 |
| Language | EN |
| Citations received | 185 |
| References cited | 1 |
Assume there are ni., i = 1, 2, *--, s, samples from s multinomial distributions each having r categories of response. Then define any u functions of the unknown true cell probabilities {7rij: i = 1, 2, * , s; j = 1, 2, * , r, where E jrij l 1 } that have derivatives up to the second order with respect to 7rij, and for which the matrix of first derivatives is of rank u. A general noniterative procedure is described for fitting these functions to a linear model, for testing the goodness-of-fit of the model, and for testing hypotheses about the parameters in the linear model. The special cases of linear functions and logarithmic functions of the 7rin are developed in detail, and some examples of how the general approach can be used to analyze various types of categorical data are presented.
Categorical variable · Combinatorics · General linear model · Generalized linear model · Goodness of fit · Linear model · Log-linear model · Logarithm · Mathematical analysis · Multinomial distribution · Rank (graph theory) · Statistics · Applied Mathematics · Mathematics · Whitehead's Philosophy and Applications
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| Unique citing works | 185 |
|---|---|
| Citations per year | 3,43 |
| Citation span | 1972 - 2021 (50) |
| Citation velocity | historical |
| Highly cited | Yes |
| Citation types | Neutral: 119 |