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interaction between continuous variables; interpretation of coefficients

To: s-news@lists.biostat.wustl.edu
Subject: interaction between continuous variables; interpretation of coefficients and plotting. Basics
From: Henrik Parn <henrik.parn@bio.ntnu.no>
Date: Thu, 17 Feb 2005 14:22:57 +0100
Organization: NTNU
Reply-to: henrik.parn@bio.ntnu.no
User-agent: Mozilla/5.0 (Windows; U; Windows NT 5.1; en-US; rv:1.7.3) Gecko/20040910
Dear S-plus experts,

I have a linear model where the response variable is survival. My focal explanatory variable is body mass, but I also include the time of the season (day.number) in the model. There is a significant interaction between the two continuous variables.

model <- lm(survival ~ mass * day.number)

The coefficients:
mass: -0.05
day.number: -0.051
mass*day.number: 0.014

From what I have heard and partly read, I have got the impression (well founded or not...?) that it is difficult to interpret the coefficients in an interaction between continuous terms. My very naive and entirely qualitative interpretation of the above results would be: There is a negative effect of mass on survival early in the season (low day.number). However as the season proceeds the positive interaction, mass*day.number, cancels the negative effect of mass. Is this correct? How do I calculate the actual value of survival for a given mass and day.number?

Can anyone please help me with a convenient way to represent the interaction graphically in S-plus and to interpret the coefficients quantitatively (analoguous to an interaction with a factor).

Thanks a lot in advance for any kinds of suggestions!

Sincerely,

Henrik Pärn

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