aldmck: Aldrich-McKelvey Scaling
In basicspace: Recovering a Basic Space from Issue Scales

Description Usage Arguments Value Author(s) References See Also Examples

aldmck is a function that takes a matrix of perceptual data, such as liberal-conservative rankings of various stimuli, and recovers the true location of those stimuli in a spatial model. It differs from procedures such as wnominate, which instead use preference data to estimate candidate and citizen positions. The procedure here, developed by John Aldrich and Richard McKelvey in 1977, is restricted to estimating data with no missing values and only in one dimension. Please refer to the blackbox and blackbox_transpose functions in this package for procedures that accomodate missing data and multidimensionality estimates.

1	aldmck(data, respondent = 0, missing=NULL, polarity, verbose=FALSE)

`data`	matrix of numeric values, containing the perceptual data. Respondents should be organized on rows, and stimuli on columns. It is helpful, though not necessary, to include row names and column names.
`respondent`	integer, specifies the column in the data matrix of the stimuli that contains the respondent's self-placement on the scale. Setting respondent = 0 specifies that the self-placement data is not available. Self-placement data is not required to estimate the locations of the stimuli, but is required if recovery of the respondent ideal points, or distortion parameters is desired. Note that no distortion parameters are estimated in AM without self-placements because they are not needed, see equation (24) in Aldrich and McKelvey (1977) for proof.
`missing`	vector or matrix of numeric values, sets the missing values for the data. NA values are always treated as missing regardless of what is set here. Observations with missing data are discarded before analysis. If input is a vector, then the vector is assumed to contain the missing value codes for all the data. If the input is a matrix, it must be of dimension p x q, where p is the maximum number of missing values and q is the number of columns in the data. Each column of the inputted matrix then specifies the missing data values for the respective variables in data. If null (default), no missing values are in the data other than the standard NA value.
`polarity`	integer, specifies the column in the data matrix of the stimuli that is to be set on the left side (generally this means a liberal)
`verbose`	logical, indicates whether `aldmck` should print out detailed output when scaling the data.

An object of class aldmck.

`legislators`	vector, containing the recovered locations of the stimuli. The names of the stimuli are attached if provided as column names in the argument `data`, otherwise they are generated sequentiall as 'stim1', 'stim2', etc.
`respondents`	matrix, containing the information estimated for each respondent. Observations which were discarded in the estimation for missing data purposes have been NA'd out: `intercept`Intercept of perceptual distortion for respondent. `weight`Weight of perceptual distortion for respondent. `idealpt`Estimated location of the respondent. Note that these positions are still calculated for individuals with negative weights, so these may need to be discarded. Note that this will not be calculated if self-placements are not provided in the data. `selfplace`The self-reported location of the individual, copied from the `data` argument if `respondent` is not set to 0. `polinfo`Estimated political information of respondent, calculated as the correlation between the true and reported stimulus locations. The validation of this measure is provided in the article by Palfrey and Poole in the references. Note that this measure is included even for respondents that were not used in the estimation. Individuals with negative weights have also been assigned a political information score of 0, rather than negative scores.
`eigenvalues`	A vector of the eigenvalues from the estimation.
`AMfit`	Ratio of overall variance to perceptions in scaled data divided by average variance. This measure of fit, described by Aldrich and McKelvey, measures the amount of reduction of the variance of the scaled over unscaled data.
`N`	Number of respondents used in the estimation (i.e. had no missing data)
`N.neg`	Number of cases with negative weights. Only calculated if respondent self-placements are specified, will equal 0 if not.
`N.pos`	Number of cases with positive weights. Only calculated if respondent self-placements are specified, will equal 0 if not.

Keith Poole ktpoole@uga.edu

Howard Rosenthal hr31@nyu.edu

Jeffrey Lewis jblewis@ucla.edu

James Lo lojames@usc.edu

Royce Carroll rcarroll@rice.edu

Keith Poole, Jeffrey Lewis, Howard Rosenthal, James Lo, Royce Carroll (2016) “Recovering a Basic Space from Issue Scales in R.” Journal of Statistical Software. 69(7), 1–21. doi:10.18637/jss.v069.i07

John H. Aldrich and Richard D. McKelvey (1977) “A Method of Scaling with Applications to the 1968 and 1972 Presidential Elections.” American Political Science Review. 71(1), 111-130.

Thomas R. Palfrey and Keith T. Poole (1987) “The Relationship between Information, Ideology, and Voting Behavior.” American Journal of Political Science. 31(3), 511-530.

Keith Poole. http://voteview.com

'LC1980', 'summary.aldmck', 'plot.aldmck', 'plot.cdf'.

### Loads and scales the Liberal-Conservative scales from the 1980 NES.
data(LC1980)
result <- aldmck(data=LC1980, polarity=2, respondent=1, missing=c(0,8,9),verbose=TRUE)
summary(result)
plot.aldmck(result)