I am well aware how to read the model summary in R for a regression model when a factor is included. The "first" level, in terms of ABC, is regarded as the base level to which all further levels of that factor are compared to. In an ANOVA-style model the baseline value is found in the intercept (equals the mean response value for base-level class).

However, if one or several factors are mixed with continuous predictors, then how can I see what the base-level values are at all? to what would I compare?

In the model output below, there are two factors:

  1. LandUse (4 Levels)
  2. Type_LU (4 Levels)

I see now for example that LandUseLow is 0.35 units higher than the base-line LandUseHigh. Would one now simply look at the mean response for the class LandUseHigh and compare? Is it that simple?

                  Estimate Std. Error Adjusted SE z value Pr(>|z|)
(Intercept)      4.6086772  1.7754606   1.7773711   2.593  0.00951 **
DiTempRange     -0.1409464  0.0764872   0.0765969   1.840  0.06575 .
LandUseLow       0.3520743  0.5989777   0.5997903   0.587  0.55721
LandUseMedium    0.2741413  0.3668149   0.3675811   0.746  0.45579
LandUseNone     -1.0128945  0.5735342   0.5744652   1.763  0.07787 .
MAP              0.0048810  0.0009128   0.0009142   5.339    1e-07 ***
Rivier           0.3502782  0.2252743   0.2257546   1.552  0.12076
TempRange        0.0823410  0.0606546   0.0607942   1.354  0.17560
Tmean           -0.1762862  0.0994486   0.0996353   1.769  0.07684 .
TYPE_LUconserva -0.9312487  0.4770681   0.4781244   1.948  0.05145 .
TYPE_LUprivate  -0.4839229  0.3289011   0.3296201   1.468  0.14207
TYPE_LUstate     0.0004062  0.4079678   0.4089744   0.001  0.99921
logVRM           0.1370973  0.1140166   0.1142342   1.200  0.23008
logTWI          -0.0735540  0.4195267   0.4202589   0.175  0.86106
logDAH           1.7132823  3.5937000   3.6028996   0.476  0.63441

@Placidia is right. However, this is a simplified case because you do not have any interactions. That is, your model assumes (rightly or wrongly) that moving from LandUseHigh to LandUseLow is associated with an increase of 0.25 units in your response variable no matter what the level of Type_LU is or what the values of your continuous covariates are.

If you did have interactions, then the coefficient on LandUseLow would correspond to the change from LandUseHigh only when Type_LU is set at the reference level. Likewise, if there were an interaction between LandUse and a continuous covariate, the coefficient on LandUseLow would correspond to the change from LandUseHigh only when the value of the continuous covariate were $0$. If you had a three-way interaction between LandUse, Type_LU and a continuous covariate, it would indicate the change when both Type_LU is set at the reference level and the value of the continuous covariate were $0$.

Update: The (intercept) indicates the value of the reference category. You have two categorical variables, so you have two reference categories. Your reference categories are LandUseHigh and an unspecified level of Type_LU (which I assume you know). So the value of the Estimate in the (intercept) row is the predicted mean for those study units in both of those categories when all the continuous covariates are equal to $0$. Again, because you don't have an interaction term, the value of LandUseHigh when Type_LU is conserva, private, or state is the sum of the estimate for the intercept plus the estimate for the appropriate level of Type_LU.

  • $\begingroup$ Dear Gung & Placidia, thank your interpretations. Sadly I think I did not write my question clear enough. I wanted to know "how do I know the baseline value to which LandUseLow is compared to?". The value of LandUseHigh is not shown in the table. Of course I can look up by hand, but how would I report this in a paper so that the reader can follow? Thank you VERY much for the hint on the interaction! I did not think about that before (+1). $\endgroup$ – Jens Jun 6 '14 at 8:34

The LandUseLow coefficient tells you what happens to the response when everything is held constant, except that land use goes from High to Low -- you then expect to see a change of 0.35.

  • $\begingroup$ Also, it's necessary to keep in mind that the comparison of LandUseLow to baseline, in the presence of continuous variables, compares LandUseLow to baseline when these continuous predictors are 0. Often, this is not reasonable, but I can't tell from the variable names. $\endgroup$ – Lost in transcription Jun 3 '14 at 17:27

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