zrl
2009-Aug-28 22:49 UTC
[R] how to explain the interaction terms regarding "treatment contrast" of lm model
Dear list, I am confused on how to explain the interaction term in the context of "treatment contrast". for example, I have an data frame as below: sub group val 1 a group1 3.685625 2 a group1 3.407445 3 a group1 4.040920 4 a group1 2.890875 5 b group1 3.853280 6 b group1 4.113585 7 b group1 3.043250 8 b group1 3.800920 9 c group1 5.394305 10 c group1 5.004290 11 c group1 4.651435 12 c group1 4.286650 13 d group1 4.773440 14 d group1 3.982200 15 d group1 5.718690 16 d group1 4.803815 ..... 45 d group3 8.021240 46 d group3 7.641685 47 d group3 7.519445 48 d group3 9.514580 then:>tapply(val,list(group,sub),mean)a b c d group1 3.506216 3.702759 4.834170 4.819536 group2 4.831503 5.246833 5.930116 6.649191 group3 6.233062 6.648325 7.787651 8.174238> summary(lm(val~group*sub))Call: lm(formula = val ~ group * sub) Residuals: Min 1Q Median 3Q Max -1.24378 -0.50184 -0.03726 0.51748 1.34034 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 3.5062 0.3278 10.696 9.98e-13 *** groupgroup2 1.3253 0.4636 2.859 0.00703 ** groupgroup3 2.7268 0.4636 5.882 9.98e-07 *** subb 0.1965 0.4636 0.424 0.67411 subc 1.3280 0.4636 2.865 0.00693 ** subd 1.3133 0.4636 2.833 0.00751 ** groupgroup2:subb 0.2188 0.6556 0.334 0.74052 groupgroup3:subb 0.2187 0.6556 0.334 0.74060 groupgroup2:subc -0.2293 0.6556 -0.350 0.72851 groupgroup3:subc 0.2266 0.6556 0.346 0.73158 groupgroup2:subd 0.5044 0.6556 0.769 0.44671 groupgroup3:subd 0.6279 0.6556 0.958 0.34460 --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Residual standard error: 0.6556 on 36 degrees of freedom Multiple R-squared: 0.8607, Adjusted R-squared: 0.8182 F-statistic: 20.22 on 11 and 36 DF, p-value: 3.296e-12 My question is: with "treatment contrast" in R, Coefficients, groupgroup2,groupgroup3, subb, subc,subd are the difference from Intercept 3.5062 (reference level for intercepts). But what is the reference level for the interaction terms? such as groupgroup2:subb,groupgroup3:subb,and etc. Thanks. [[alternative HTML version deleted]]
Daniel Malter
2009-Aug-29 00:02 UTC
[R] how to explain the interaction terms regarding "treatmentcontrast" of lm model
The intercept is group=1, sub=a, The interaction between sub=b and group=2 implies that both sub=b and group=2 direct effects are included. That is, with the direct effects only you are now at: intercept+group2+subb, which means the intercept (group1 and sub=a) + the average difference between group=2 and group=1 + the average difference between sub=b and sub=a. This is the reference level for the interaction effect between group=2 and sub=b. This is not one-specific group in your experiment but rather a generic average group (average group=2, average sub=b). Your interaction effect now asks the question how much does group=2 with sub=b stand out from the average in its group and in its sub. To clarify your confusion, you may want to write out the model formula. Daniel ------------------------- cuncta stricte discussurus ------------------------- -----Urspr?ngliche Nachricht----- Von: r-help-bounces at r-project.org [mailto:r-help-bounces at r-project.org] Im Auftrag von zrl Gesendet: Friday, August 28, 2009 6:49 PM An: r-help Betreff: [R] how to explain the interaction terms regarding "treatmentcontrast" of lm model Dear list, I am confused on how to explain the interaction term in the context of "treatment contrast". for example, I have an data frame as below: sub group val 1 a group1 3.685625 2 a group1 3.407445 3 a group1 4.040920 4 a group1 2.890875 5 b group1 3.853280 6 b group1 4.113585 7 b group1 3.043250 8 b group1 3.800920 9 c group1 5.394305 10 c group1 5.004290 11 c group1 4.651435 12 c group1 4.286650 13 d group1 4.773440 14 d group1 3.982200 15 d group1 5.718690 16 d group1 4.803815 ..... 45 d group3 8.021240 46 d group3 7.641685 47 d group3 7.519445 48 d group3 9.514580 then:>tapply(val,list(group,sub),mean)a b c d group1 3.506216 3.702759 4.834170 4.819536 group2 4.831503 5.246833 5.930116 6.649191 group3 6.233062 6.648325 7.787651 8.174238> summary(lm(val~group*sub))Call: lm(formula = val ~ group * sub) Residuals: Min 1Q Median 3Q Max -1.24378 -0.50184 -0.03726 0.51748 1.34034 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 3.5062 0.3278 10.696 9.98e-13 *** groupgroup2 1.3253 0.4636 2.859 0.00703 ** groupgroup3 2.7268 0.4636 5.882 9.98e-07 *** subb 0.1965 0.4636 0.424 0.67411 subc 1.3280 0.4636 2.865 0.00693 ** subd 1.3133 0.4636 2.833 0.00751 ** groupgroup2:subb 0.2188 0.6556 0.334 0.74052 groupgroup3:subb 0.2187 0.6556 0.334 0.74060 groupgroup2:subc -0.2293 0.6556 -0.350 0.72851 groupgroup3:subc 0.2266 0.6556 0.346 0.73158 groupgroup2:subd 0.5044 0.6556 0.769 0.44671 groupgroup3:subd 0.6279 0.6556 0.958 0.34460 --- Signif. codes: 0 *** 0.001 ** 0.01 * 0.05 . 0.1 1 Residual standard error: 0.6556 on 36 degrees of freedom Multiple R-squared: 0.8607, Adjusted R-squared: 0.8182 F-statistic: 20.22 on 11 and 36 DF, p-value: 3.296e-12 My question is: with "treatment contrast" in R, Coefficients, groupgroup2,groupgroup3, subb, subc,subd are the difference from Intercept 3.5062 (reference level for intercepts). But what is the reference level for the interaction terms? such as groupgroup2:subb,groupgroup3:subb,and etc. Thanks. [[alternative HTML version deleted]]