`This request has generated no replies as yet, and it's not hard to see
``why. Note, especially "I need a pretty graph"
`

`I looked up "pretty graph" in Stata and there's no routine available,
``so we'll have to think this one out. Apologies - this is a long post.
`
On 14 Noll 2008, at 16:41, Susanna Khavul wrote:

I would like to graph a quadratic interaction after running rreg
(Robust Regression). The model is as follows:
xi:rreg Y i.X1 X2 X3 X4 X5 X5squared X5*X4 X5squared*X4
(interaction terms are centered)
Where:
X5 -- independent variable
X5squared--square of the independent variable
X4-moderator
X5*X4--independent variable x moderator
X5squared*X4--independent variable squared x moderator
The rest (X1 X2 X3) are controls which I want to account for as well.
One standard deviation above and below the mean would be fine.
I want to include both components of the interaction (linear and
quadratic). Is there a module that will do it? If not, what is the
optimum graphing command.
Any help would be much appreciated. I need a pretty graph.

`It appears that X2, X3 and X4 are binary and that X1 has more than two
``categories. Even more difficult, X5 enters two interaction terms.
`

`Of course, there's no general answer to this, and a graph can only be
``constructed on the basis of the scientific question that the analysis
``answers.
`

`The first question is whether any of the predictor variables defines
``subsets of the data which are of primary interest. There may be two
``reasons for this
``1. The relationship is different in each subset. For example, in our
``National Health and Lifestyle Survey, we found that the relationship
``of well-being to age was different in men and women. In men, it
``declined continuously, while in women it declined sharply initially
``than recovered in middle and later life.
``2. There may be a priori reasons for testing the hypothesis in two
``subsets. We've got a paper in press looking at the effect of worry on
``quality of life. because of its association with depression, we have
``graphed this relationship in the depressed and the non-depressed
``participants, side by side, to show that the relationship is similar
``in depressed and non-depressed people, but that the depressed have a
``worse baseline quality of life. (Interestingly, non-depressed severe
``worriers have a quality of life just as bad as non-worried depressed
``people).
`

`If either of these two conditions is true, you probably need to
``construct a chart using -by- to make separate graphs for each subgroup
`

`The second question is whether any of the covariates can be
``'standardised out' By this I mean constructing the graphs at a chosen
``value of the covariate.
`

`For example, worry declines very significanly with age, as does
``quality of life. For this reason, we constructed our graphs of quality
``of life for a person aged 75 (using -adjust-). With continuous
``predictors which are not of primary interest, but which must be
``controlled as confounders, graphing relationships at fixed (sensible)
``values of the predictors may be the best way of displaying the data.
`

`The same logic may be applied to binary predictors, again using -
``adjust- to generate predictions for fixed prevalences of the predictors.
`
This leaves us with the final question of the form of the graph.

`Again, without knowing the science behind the question, it's
``impossible to answer. However, adding one standard deviation above and
``below the mean is probably not a good data display. The standard
``deviation measures the scatter of observations, and if you're going to
``show scatter, then you are probably better off graphing the actual
``data, whose scatter can be quite different to that implied by the
``standard deviation. Adding boxes or means plus confidence intervals
``allows you to superimpose a data summary (both implemented in Nick
``Cox's remarkably useful -stripplot-, which is the first user-written
``graphic routine I require my students to download).
`

`That's as much as I can say about the graph based on general
``principle. A good graph shows something interesting about the data. To
``make a good graph, you must first identify that interesting something.
``And this, clearly, is impossible in the absence of knowing either the
``hypothesis or the results of the analysis.
`

`However, I would be wary of -rreg- as a primary analysis tool. It is a
``good procedure for reassuring yourself that the results of your
``analysis would not change substantively if influential observations
``were down-weighted, but as a primary model-building tool it suffers, I
``think, from a primary difficulty: that it violates the logic of
``hypothesis testing.
`

`In a hypothesis test, the investigator specifies the form of the model
``and then calculates the model parameters. For example, the model
`

`baby weight = a constant + (mother's height x something1) +
``(gestational age x something2) + error
`

`needs three parameters calculated. For each parameter, we can test
``whether the proportional reduction in error is statistically
``significant.
`

`However, robust regression rebuilds the model as a complex equation in
``which individual observations are entered in a reweighted form. Thus,
``the investigator is leaving the selection of the model itself to
``chance features of the data. As such, the hypothesis tests which
``follow violate the central assumption of any such test - that the
``model was specified independently of the data.
`

`Perhaps I'm being a little jaundiced here, but I use -rreg- for
``support, not illumination.
`
Ronan Conroy
=================================
rconroy@rcsi.ie
Royal College of Surgeons in Ireland
Epidemiology Department,
Beaux Lane House, Dublin 2, Ireland
+353 (0)1 402 2431
+353 (0)87 799 97 95
+353 (0)1 402 2764 (Fax - remember them?)
http://rcsi.academia.edu/RonanConroy
P Before printing, think about the environment
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