{smcl} {hline} help for {hi:nlhockey} {hline} {title:"Hockey Stick" Regression} {p 4 8 2} {cmd:nl hockey} {it:yvar} {it:xvar1} [{it:xvarlist}] [, {cmdab:l:eft0} {cmdab:r:ight0}] {title:Description} {p 4 4 2} This command uses piecewise linear or "hockey stick" regression. It assumes that the effect of {it:xvar1} can best be fitted by two straight lines, with different slopes, and calculates the two slopes and the value of {it:xvar1} at which the slope changes (the breakpoint). {title:Options} {p 4 8} {cmdab:r:ight0} constrains the slope to the right of the breakpoint to be 0. {p_end} {p 4 8} {cmdab:l:eft0} constrains the slope to the left of the breakpoint to be 0. {p_end} {title:Remarks} {p 4} If called with just {it:yvar} and {it:xvar1}, {cmd:nlhockey} fits the model {centre:{it:yvar} = a + b*{it:xvar1} if {it:xvar1} <= c} {centre:{it:yvar} = d + e*{it:xvar1} if {it:xvar1} >= c} {p} This model requires 5 parameters, but since we want the two lines to meet when {it:xvar1} = c, there is a constraint on the parameters {centre:a + b*c = d + e*c} {p} so the model has only 4 degrees of freedom. The parameters estimated by the model are a, b, c and e: if d is of interest it must be calculated from the other parameters. In the output of nlhockey, the three parameters relating to {it:xvar1} (c, b and e) are given first, called breakpoint, slope_l and slope_r respectively. Then any coefficients for variables in {it:xvarlist}, and finally parameter a (called cons). {p 4} If {it:varlist} is included in the model, it is assumed that there is a linear association between these variables and {it:yvar}, so the models fitted become {centre:{it:yvar} = a + b*{it:xvar1} + f*{it:xvar2} if {it:xvar1} <= c} {centre:{it:yvar} = d + e*{it:xvar1} + f*{it:xvar2} if {it:xvar1} >= c} {p} i.e. only one extra parameter is estimated for each of these variables. {p 4} There is a short quadratic section between the two straight lines, to ensure that the derivative of the predictor function w.r.t {it:xvar1} is continuous at the break point. By default, the width of this quadratic section is 1/100 times the range of {it:xvar1}, but it can be changed by setting the global variable \$eps. {p 4} The options {cmd:left0} and {cmd:right0} force the constraints b = 0 and e = 0 respectively. Specifying both of these options is an error. Also, specifying either of them inappropriately can lead to odd results: if {cmd:left0} is specified and the slope for small values of {it:xvar1} is non-zero, the breakpoint c may be set less than the minimum value of {it:xvar1} in the dataset. The model is then no longer identified: for any given breakpoint, there is an intercept a which gives exactly the same model a simple linear regression. You should run {cmd:loghockey} without either of these options first, and only if the parameter estimates and standard errors from this model convince you should you specify either of these options. {title:References} {p 4 } The code in nlhockey.ado is based very closely on the Splus code by Mary Lindstrom that was posted to the S-news mailing list, April 24, 2000. Also see {p} Bacon & Watts "{it:Estimating the Transition Between Two Intersecting Straight Lines}", Biometrika, 1971. {title:Author} {p 4 4 2} Mark Lunt, Arthritis Research UK Epidemiology Unit {p 4 4 2} The University of Manchester {p 4 4 2} Please email {browse "mailto:mark.lunt@manchester.ac.uk":mark.lunt@manchester.ac.uk} if you encounter problems with this program.