# How to do regression with effect coding instead of dummy coding in R?

I am currently working on a regression model where I have only categorical/factor variables as independent variables. My dependent variable is a logit transformed ratio.

It is fairly easy just to run a normal regression in R, as R automatically know how to code dummies as soon as they are of the type "factor". However this type of coding also implies that one category from each variable is used as a baseline, making it hard to interpret.

My professor have told me to just use effect coding instead (-1 or 1), as this implies the use of the grand mean for the intercept.

Does anyone know how to handle that?

Until now I have tried:

gm <- mean(tapply(ds$ln.crea, ds$month,  mean))
model <- lm(ln.crea ~ month + month*month + year + year*year, data = ds, contrasts = list(gm = contr.sum))

Call:
lm(formula = ln.crea ~ month + month * month + year + year *
year, data = ds, contrasts = list(gm = contr.sum))

Residuals:
Min       1Q   Median       3Q      Max
-0.89483 -0.19239 -0.03651  0.14955  0.89671

Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -3.244493   0.204502 -15.865   <2e-16 ***
monthFeb    -0.124035   0.144604  -0.858   0.3928
monthMar    -0.365223   0.144604  -2.526   0.0129 *
monthApr    -0.240314   0.144604  -1.662   0.0993 .
monthMay    -0.109138   0.144604  -0.755   0.4520
monthJun    -0.350185   0.144604  -2.422   0.0170 *
monthJul     0.050518   0.144604   0.349   0.7275
monthAug    -0.206436   0.144604  -1.428   0.1562
monthSep    -0.134197   0.142327  -0.943   0.3478
monthOct    -0.178182   0.142327  -1.252   0.2132
monthNov    -0.119126   0.142327  -0.837   0.4044
monthDec    -0.147681   0.142327  -1.038   0.3017
year1999     0.482988   0.200196   2.413   0.0174 *
year2000    -0.018540   0.200196  -0.093   0.9264
year2001    -0.166511   0.200196  -0.832   0.4073
year2002    -0.056698   0.200196  -0.283   0.7775
year2003    -0.173219   0.200196  -0.865   0.3887
year2004     0.013831   0.200196   0.069   0.9450
year2005     0.007362   0.200196   0.037   0.9707
year2006    -0.281472   0.200196  -1.406   0.1625
year2007    -0.266659   0.200196  -1.332   0.1855
year2008    -0.248883   0.200196  -1.243   0.2164
year2009    -0.153083   0.200196  -0.765   0.4461
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 0.3391 on 113 degrees of freedom
Multiple R-squared: 0.3626, Adjusted R-squared: 0.2385
F-statistic: 2.922 on 22 and 113 DF,  p-value: 0.0001131


In principle, there are two types of contrast coding, with which the intercept will estimate the Grand Mean. These are sum contrasts and repeated contrasts (sliding differences).

Here's an example data set:

set.seed(42)
x <- data.frame(a = c(rnorm(100,2), rnorm(100,1),rnorm(100,0)),
b = rep(c("A", "B", "C"), each = 100))


The conditions' means:

tapply(x$a, x$b, mean)
A           B           C
2.03251482  0.91251629 -0.01036817


The Grand Mean:

mean(tapply(x$a, x$b, mean))
[1] 0.978221


You can specify the type of contrast coding with the contrasts parameter in lm.

Sum contrasts

lm(a ~ b, x, contrasts = list(b = contr.sum))

Coefficients:
(Intercept)           b1           b2
0.9782       1.0543      -0.0657


The intercept is the Grand Mean. The first slope is the difference between the first factor level and the Grand Mean. The second slope is the difference between the second factor level and the Grand Mean.

Repeated contrasts

The function for creating repeated contrasts is part of the MASS package.

lm(a ~ b, x, contrasts = list(b = MASS::contr.sdif))

Coefficients:
(Intercept)         b2-1         b3-2
0.9782      -1.1200      -0.9229


The intercept is the Grand Mean. The slopes inidcate the differences between consecutive factor levels (2 vs. 1, 3 vs. 2).

• Hmm, just tried out what you suggested, but I am not sure any of the codes does what I want. The thing is that I have years {1998, ... , 2007} in one IV and months{Jan, ... , Dec} in another IV. As it is now the lm function automatically let April become the intercept as well as 1998. Instead i just want the intercept to be an overall mean... I do not really know if it makes sense when thinking about it... – Kasper Christensen Mar 13 '13 at 21:18
• @KasperChristensen If you specify the contrasts like in the examples, the intercept will be the Grand Mean. Please provide a reproducible example of what you've tried. – Sven Hohenstein Mar 13 '13 at 21:25
• @SvenHohenstein why is there no b3 coefficient for C categorical value in sum contrasts? It should be -0.9885891. – Vivaldi Jul 12 '18 at 9:53
• @Vivaldi The value of b3 is determined by the the intercept and b1, b2. There is no degree of freedom left for another contrast. – Sven Hohenstein Jul 12 '18 at 11:41
• @SvenHohenstein Isn't this more a collinearity problem since b3 can be directly expressed as a linear combination of other variables: (3*grand mean - b1 - b2)? – Vivaldi Jul 12 '18 at 12:32

Nitpicking: if your professor told you to code your variables with (-1, 1), he told you to use effect coding, not effect sizes. At any rate, @user20650 is right. As usual, the UCLA stats help website has a useful page the explains how to do this with R.