“Ridit scoring”的意思、由来-开放百科全书

词条

Ridit scoring

释义

Calculation of ridit scores
Choosing a reference data set Determining the probability function Determining ridits
Interpretation and examples
Applications
A mathematical approach
See also
Notes
Further reading

In econometrics, ridit scoring is a statistical method used to analyze ordered qualitative measurements.

The tools of ridit analysis were developed and first applied by Bross,^[1] who coined the term "ridit" by analogy with other statistical transformations such as probit and logit.

Calculation of ridit scores

Choosing a reference data set

Since ridit scoring is used to compare two or more sets of ordered qualitative data, one set is designated as a reference against which other sets can be compared. In econometric studies, for example, the ridit scores measuring taste survey answers of a competing or historically important product are often used as the reference data set against which taste surveys of new products are compared. Absent a convenient reference data set, an accumulation of pooled data from several sets or even an artificial or hypothetical set can be used.

Determining the probability function

After a reference data set has been chosen, the reference data set must be converted to a probability function. To do this, let x₁, x₂,..., x_n denote the ordered categories of the preference scale. For each j, x_j represents a choice or judgment. Then, let the probability function p be defined with respect to the reference data set as

Determining ridits

The ridit scores, or simply ridits, of the reference data set are then easily calculated as

Each of the categories of the reference data set are then associated with a ridit score.

More formally, for each , the value w_j is the ridit score of the choice x_j.

Interpretation and examples

Intuitively, ridit scoring can be understood as a modified notion of percentile. For any j, if x_j has a low (close to 0) ridit score, one can conclude that

is very small, which is to say that very few respondents have chosen a category "lower" than x_j.

Applications

Ridit scoring has found use primarily in the health sciences (including nursing and epidemiology) and econometric preference studies.{{Citation needed|date=June 2011}}

A mathematical approach

Besides having intuitive appeal, the derivation for ridit scoring can be arrived at with mathematically rigorous methods as well. Brockett and Levine^[2] presented a derivation of the above ridit score equations based on several intuitively uncontroversial mathematical postulates.

Notes

R statistical computing package for Ridit Analysis: https://cran.r-project.org/package=Ridit

1. ^Bross, Irwin D.J. (1958) "How to Use Ridit Analysis," Biometrics, 14 (1):18-38 {{jstor|2527727}}
2. ^Brockett, Patrick L. and Levine, Arnold (1977) "On a Characterization of Ridits," The Annals of Statistics, 5 (6):1245-1248 {{jstor|2958658}}