# st: Re: interactions, slopes, and standard errors

 From Jeffrey Simons <[email protected]> To <[email protected]> Subject st: Re: interactions, slopes, and standard errors Date Sat, 27 Mar 2004 08:31:53 -0600

```Has anyone written a general program to calculate and display the estimated
slope and associated error of Y on x1 at various values of x2, where Y = b0
+ b1x1 + b2x2 + b3x1x2

Last fall Scott Merryman posted a nice program (which I copy in, below)
which takes care of this at the mean of x2. Thanks, Scott!, We could also
be interested in doing it for other values.

Chip Hunter

I have written a program that does this and makes graphs or the simple
slopes at various multiples of the SD of x2. It will do it for several forms
of interactions, e.g., 2-way, 3-way, quadratic effects etc. The help file is
below. I'd be happy to make it available to anyone interested but thought it
could still use some more refinement.

Jeffrey Simons

{smcl}
{.-}
help for {cmd:sslope}
{.-}

{title:Simple Slope Calculation for Linear Regression}

{p 8 8}
{cmd:sslope}
{it:varlist}
[{cmd:if} {it:exp}] [{cmd:in} {it:range}]
{cmd:,}
[{cmd:i}{cmd:(}{it:x z xz}{cmd:)}]
[{cmd:i}{cmd:(}{it:x z w xz xw zw xzw}{cmd:)}]
[{cmd:i}{cmd:(}{it:x x-squared}{cmd:)}]
[{cmd:i}{cmd:(}{it:x z x-squared xz}{cmd:)}]
[{cmd:i}{cmd:(}{it:z x x-squared xz}{cmd:)}]
[{cmd:sd}{cmd:(}{it:#}{cmd:)}]
[{cmd:Graph}] or [{cmd:go(}{cmd:}graph options{cmd:)}]
[{cmd:Fits}]

{p 8 27}
{it:varlist} = regression equation with {ul:centered variables} including
all interactions

{p 8 8}
option {cmd:i} must include either
{cmd:(x z xz)}  (2-way interaction), gives slope of criterion variable on x
at levels of z
(x z xz are variable names)

{p 8 8}
OR

{p 8 8}
{cmd:(x z w xz xw zw xzw)}  (3-way interaction), gives slope of criterion
variable on x
at levels of z and w

{p 8 8}
OR

{p 8 8}
{cmd:(x x-squared)}  (quadratic), gives slope of criterion variable on x
at levels of x. Also calculates the minimum or maximum of the curve.

{p 8 8}
OR

{p 8 8}
{cmd:(x z x-squared xz)}  (quadratic plus linear interaction), gives slope
of criterion variable on x
at levels of x and z. Also calculates the minumum or maximum of the curves.

{p 8 8}
OR

{p 8 8}
{cmd:(z x x-squared xz)}  (quadratic plus linear interaction), gives slope
of criterion variable on z
at levels of x.

{title:Description}

{p}
This calculates simple slopes for interactions between continuous variables
in linear regression analysis.
For example, the slope of the criterion on x conditional upon z. All
continuous variables in the regression
must be centered at the mean. The simple slope of interest must be specified
in {cmd:i}. This must be of the
form x(slope of interest) z(moderating variable) xz(the interaction between
the two). Hence, {cmd:i}(x z xz)
provides a different result than {cmd:i}(z x xz). Both are correct, one is
the slope of y on x conditional upon z
and the other, the slope of y on z conditional upon x. However, {cmd:i}(x xz
z) will produce incorrect results.
Similarly, for a three-way interaction, {cmd:i} must be in the form of (x z
w xz xw zw xzw) for the slope of x
conditional upon z and w. {ul:Important}, the order i(x z w xz {it:wz} xw
xzw) will not produce the correct
results. The order is x (slope of interest) z w (first order terms of the
moderators) x^2 (x quadratic term) xz xw (2-way interactions
with x) zw (the 2-way interaction of the moderators without x) xzw (the
three way interaction). The order
of variables in varlist does not matter but calculations of the simple
slopes depend upon the specified order
in {cmd:i}. Simple slopes associated with both an interaction and a
(i.e., y on x when there are both xz and x-squared terms) are not supported
at this time.
The calculations are based upon the formulas provided in Aiken & West
(1991).

{title:Options}

{p}
{cmd:sd}{cmd:(#)} specifies the conditional levels of interest of z and/or
w, in sd units, default = 1.0.

{p}
{cmd:Graph} requests a graph of the conditional slopes. Continuous variables
not included in the interaction
are held constant at mean=0, if there are dichotomous variables in the
model, this option creates graphs
for a category=0, if there is not a category=0, the intercepts will be
invalid.

{p}
{cmd:go} requests a graph as above, but accepts all standard graph options
for {cmd:scatter}.
Choose either {cmd:Graph} for the default graph OR {cmd:go} and define graph
options.

{p}
{cmd:Fits} requests the conditional fitted values be saved. This is included

{p}
{title:Examples}

sslope y x z xz, i(x z xz)
sslope y x z xz, i(x z xz) sd(2)
sslope y x z w xz xw zw xzw, i(x z w xz xw zw xzw)
sslope y q x z w xz, i(x z xz)
sslope y x x-squared, i(x x-squared) graph
sslope y x z x-squared, i(x x-squared) graph fits
sslope y x q z  xz x-squared, i(x z x-squared xz) go(sort c(. l l l) m(o i i
i) mlabel(id)) fits

{bf}
{dialog sslope:sslope dialog box}

{bf}Author

{sf}Jeffrey S. Simons - [email protected]

{bf}Also see

{help mcenter}

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```