## NAME

emmethod -- Compute linear regression for censored data by EM method

## USAGE

`emmethod input`

## DESCRIPTION

The `emmethod' task calculates linear regression coefficients assuming a normal distribution of residuals. The EM algorithm can treat several independent variables if the dependent variable contains only one kind of censoring (i.e., upper or lower limits). There is considerable uncertainty regarding the error analysis of the regression coefficients of the EM method. This task uses analytic formulae based on asymptotic normality.

## PARAMETERS

- input [string]
- Input file(s); this can be a list of files. Following each file name is a list of column names in brackets. These column names specify which columns in the file contain the information used by this task. The brackets MUST contain at least three names in the following format: [censor_indicator, independent_vars, dependent_vars]. If there is more than one independent variable, the column names all follow the censor indicator. The list should only contain one column of dependent variables, which must be the last column in the brackets. The censor indicator specifies the censorship of the data point. The different kinds of censorship are explained in the `censor' help file. If the input file is a table, the names in brackets are the table column names. If the input file is a text file, the names in brackets are the column numbers. A title string will be printed if the input file is a table containing the header parameter "TITLE".

- alpha = "0.0" [string]
- This parameter is not used unless the value of the task parameter
"emestim" is set to "yes". If it is, this parameter will provide
initial estimates of the regression coefficients.
Coefficients should be entered as a comma separated list. The first coefficient should be the estimate of the intercept and the rest of the coefficients should be the estimates of the slopes of the independent variables. If the number of values in the list is less than the number of coefficients, remaining coefficients will be set to zero. If the number of values in the list is greater than the number of coefficients, the extra values will be ignored.

- (tolerance = 1.0E-5) [real, min=0.]
- Tolerance for regression fit. If the difference between two successive estimates of the regression coefficients is less than this value for all coefficients, the iteration stops.

- (niter = 50) [integer, min=1]
- Maximum number of iterations. The computation stops when the maximum number of iterations is performed even if convergence has not been achieved.

- (emestim = no) [boolean]
- User provides initial values for regression coefficients? If you have good estimates of the coefficients, say from a previous run, then you may want to set this to "yes".

- (verbose = no) [boolean]
- Provide detailed output? The detailed output includes the number of data points and the number of censored points and type of censorship.

## EXAMPLES

1. Apply `emmethod' to the data in the table "kriss.tab", using the columns "Censor" for the censoring indicator, "LogL1mu" for the first independent variable column, "LogL2500A" for the second independent variable column, and "LogL2keV" for the dependent variable column. Then use the file "iraslum.dat" (text file), columns 1, 2, and 3 (censor, independent, dependent). Several files may be processed sequentially. The following will compute the EM algorithm linear regression fit for the two files indicated:

cl> emmethod kriss.tab[Censor,LogL1mu,LogL2500A,LogL2keV], \ >>> iraslum.dat[1,2,3]

## BUGS

The code for this task allows a censor indicator of 5, which flags a dependent variable that is confined between two values. In this case, the input would contain two columns of dependent variables, one for the lower limit and the other for the upper limit. This option has not been adequately tested, however, and in fact it has been known to fail.

## SEE ALSO

censor, survival

Type "help statistics option=sys" for a higher-level description of the `statistics' package.