SSI: Similar Student Index
In wasabi1989/MiscPsycho: Miscellaneous Psychometric Analyses

Description Usage Arguments Details Value Author(s) Examples

The similar student index uses a K nearest neighbor algorithm to generate a set of conditional norms for the outcome variable. The conditional norm is constructed on the basis of the K students in the data most like student i who are used as the comparison set

SSI(...)
## Default S3 method:
SSI(mf, y, k, ...)
## S3 method for class 'formula'
SSI(formula, data, id, k, na.action, subset, ...)

`formula`	a formula of the form `lhs ~ rhs` where `lhs` is a numeric variable giving the data values and `rhs` also numeric variables giving the `conditioning` variables used to identify the nearest neighbor.
`data`	an optional data frame, list or environment (or object coercible by `as.data.frame` to a data frame) containing the variables in the model. If not found in `data`, the variables are taken from `environment(formula)`, typically the environment from which `SSI` is called.
`na.action`	a function which indicates what should happen when the data contain `NA`s. Defaults to `getOption("na.action")`.
`subset`	an optional vector specifying a subset of observations to be used.
`id`	the individual (student) id identifying records in the data
`k`	the number of nearest neighbors to choose. k cannot be larger than the total number of pairwise comparisons in the data.
`mf`	a model frame with the variables used for conditioning. Only implemented for the default method.
`y`	the numeric outcome variable. Only implemented for the default method
`...`	Not implemented

Implementation of the K nearest neighbor method is based on the euclidean distance metric. Because the process identifies the k nearest neighbors for each record in the data, the process can be relatively slow, executing in O(n^2logn)

A list with class "SSI" containing the following components:

`Zscore`	the conditional `z`-score for each record in the data)
`percentile`	the conditional percentile for each reocrd in the data
`ID`	the individual's record id
`Iterations`	the number of Newton-Raphson iterations used
`model.frame`	the data matrix used for estimating the conditional norms. This data frame can differ from the original data depending on the use of `na.action`.

Harold Doran

## Generate sample data
## construct a norm for the math score based on the k = 20
## other individuals in the data most like student i. 
## readScore and scienceScore are used as the conditioning variables
## to compute the euclidean norm.
set.seed(1234)
tmp <- data.frame(ID = 1:100, mathScore = rnorm(100), readScore = rnorm(100), scienceScore = rnorm(100))
(result <- SSI(mathScore ~ readScore + scienceScore, tmp, k = 20, id=ID, na.action = na.omit))
summary(result)
str(result)
head(result$model.frame)