Contrasts and linear functions of EMMs

These methods provide for follow-up analyses of emmGrid objects: Contrasts, pairwise comparisons, tests, and confidence intervals. They may also be used to compute arbitrary linear functions of predictions or EMMs.

Usage

contrast(object, ...)

# S3 method for emmGrid
contrast(object, method = "eff", interaction = FALSE, by,
  offset = NULL, scale = NULL, name = "contrast",
  options = get_emm_option("contrast"), type, adjust, simple,
  combine = FALSE, ratios = TRUE, parens, enhance.levels = TRUE, wts,
  ...)

# S3 method for emmGrid
pairs(x, reverse = FALSE, ...)

# S3 method for emmGrid
coef(object, ...)

# S3 method for emmGrid
weights(object, ...)

Arguments

object: An object of class emmGrid
...: Additional arguments passed to other methods
method: Character value giving the root name of a contrast method (e.g. "pairwise" -- see emmc-functions). Alternatively, a function of the same form, or a named list of coefficients (for a contrast or linear function) that must each conform to the number of results in each by group. In a multi-factor situation, the factor levels are combined and treated like a single factor.
interaction: Character vector, logical value, or list. If this is specified, method is ignored. See the “Interaction contrasts” section below for details.
by: Character names of variable(s) to be used for ``by'' groups. The contrasts or joint tests will be evaluated separately for each combination of these variables. If object was created with by groups, those are used unless overridden. Use by = NULL to use no by groups at all.
offset, scale: Numeric vectors of the same length as each by group. The scale values, if supplied, multiply their respective linear estimates, and any offset values are added. Scalar values are also allowed. (These arguments are ignored when interaction is specified.)
name: Character name to use to override the default label for contrasts used in table headings or subsequent contrasts of the returned object.
options: If non-NULL, a named list of arguments to pass to update.emmGrid, just after the object is constructed.
type: Character: prediction type (e.g., "response") -- added to options
adjust: Character: adjustment method (e.g., "bonferroni") -- added to options
simple: Character vector or list: Specify the factor(s) not in by, or a list thereof. See the section below on simple contrasts.
combine: Logical value that determines what is returned when simple is a list. See the section on simple contrasts.
ratios: Logical value determining how log and logit transforms are handled. These transformations are exceptional cases in that there is a valid way to back-transform contrasts: differences of logs are logs of ratios, and differences of logits are odds ratios. If ratios = TRUE and summarized with type = "response", contrast results are back-transformed to ratios whenever we have true contrasts (coefficients sum to zero). For other transformations, there is no natural way to back-transform contrasts, so even when summarized with type = "response", contrasts are computed and displayed on the linear-predictor scale. Similarly, if ratios = FALSE, log and logit transforms are treated in the same way as any other transformation.
parens: character or NULL. If a character value, the labels for levels being contrasted are parenthesized if they match the regular expression in parens[1] (via grep). The default is emm_option("parens"). Optionally, parens may contain second and third elements specifying what to use for left and right parentheses (default "(" and ")"). Specify parens = NULL or parens = "a^" (which won't match anything) to disable all parenthesization.
enhance.levels: character or logical. If character, the levels of the named factors that are contrasted are enhanced by appending the name of the factor; e.g., if a factor named "trt" has levels A and B, a trt comparison is labeled trtA - trtB. If enhance.levels is logical, then if TRUE (the default), only factors with numeric levels are enhanced; and of course if FALSE, no levels are enhanced. The levels of by variables are not enhanced, and any names of factors that don't exist are silently ignored. To enhance the labels beyond what is done here, change them directly via levels<-.
wts: The wts argument for some contrast methods. You should omit this argument unless you want unequal wts. Otherwise we recommend specifying wts = NA which instructs that wts be obtained from object, separately for each by group. If numerical wts are specified, they must conform to the number of levels in each by group, and those same weights are used in each group.
x: An emmGrid object
reverse: Logical value - determines whether to use "pairwise" (if TRUE) or "revpairwise" (if FALSE).

Value

contrast and pairs return an object of class

emmGrid. Its grid will correspond to the levels of the contrasts and any by variables. The exception is that an emm_list

object is returned if simple is a list and combine is

FALSE.

coef returns a data.frame containing the "parent" object's grid, along with columns named c.1, c.2, ... containing the contrast coefficients used to produce the linear functions embodied in the object. coef() only returns coefficients if object is the result of a call to contrast(), and the parent object is the object that was handed to contrast. This is most useful for understanding interaction contrasts.

weights returns the weights stored for each row of object, or a vector of 1s if no weights are saved.

Note

When object has a nesting structure (this can be seen via str(object)), then any grouping factors involved are forced into service as by variables, and the contrasts are thus computed separately in each nest. This in turn may lead to an irregular grid in the returned emmGrid object, which may not be valid for subsequent emmeans calls.

Pairs method

The call pairs(object) is equivalent to contrast(object, method = "pairwise"); and pairs(object, reverse = TRUE) is the same as contrast(object, method = "revpairwise").

Interaction contrasts

When interaction is specified, interaction contrasts are computed. Specifically contrasts are generated for each factor separately, one at a time; and these contrasts are applied to the object (the first time around) or to the previous result (subsequently). (Any factors specified in by are skipped.) The final result comprises contrasts of contrasts, or, equivalently, products of contrasts for the factors involved. Any named elements of interaction are assigned to contrast methods; others are assigned in order of appearance in object@levels. The contrast factors in the resulting emmGrid object are ordered the same as in interaction.

interaction may be a character vector or list of valid contrast methods (as documented for the method argument). If the vector or list is shorter than the number needed, it is recycled. Alternatively, if the user specifies contrast = TRUE, the contrast specified in method is used for all factors involved.

Simple contrasts

simple is essentially the complement of by: When simple is a character vector, by is set to all the factors in the grid except those in simple. If simple is a list, each element is used in turn as simple, and assembled in an "emm_list". To generate all simple main effects, use simple = "each" (this works unless there actually is a factor named "each"). Note that a non-missing simple will cause by to be ignored.

Ordinarily, when simple is a list or "each", the return value is an emm_list object with each entry in correspondence with the entries of simple. However, with combine = TRUE, the elements are all combined into one family of contrasts in a single emmGrid object using rbind.emmGrid.. In that case, the adjust argument sets the adjustment method for the combined set of contrasts.

Examples

warp.lm <- lm(breaks ~ wool*tension, data = warpbreaks)
(warp.emm <- emmeans(warp.lm, ~ tension | wool))
#> wool = A:
#>  tension emmean   SE df lower.CL upper.CL
#>  L         44.6 3.65 48     37.2     51.9
#>  M         24.0 3.65 48     16.7     31.3
#>  H         24.6 3.65 48     17.2     31.9
#> 
#> wool = B:
#>  tension emmean   SE df lower.CL upper.CL
#>  L         28.2 3.65 48     20.9     35.6
#>  M         28.8 3.65 48     21.4     36.1
#>  H         18.8 3.65 48     11.4     26.1
#> 
#> Confidence level used: 0.95 

contrast(warp.emm, "poly")    # inherits 'by = "wool"' from warp.emm
#> wool = A:
#>  contrast  estimate   SE df t.ratio p.value
#>  linear      -20.00 5.16 48  -3.878  0.0003
#>  quadratic    21.11 8.93 48   2.363  0.0222
#> 
#> wool = B:
#>  contrast  estimate   SE df t.ratio p.value
#>  linear       -9.44 5.16 48  -1.831  0.0733
#>  quadratic   -10.56 8.93 48  -1.182  0.2432
#> 

### Custom contrast coefs (we already have wool as 'by' thus 3 means to contrast)
contrast(warp.emm, list(mid.vs.ends = c(-1,2,-1)/2, lo.vs.hi = c(1,0,-1)))
#> wool = A:
#>  contrast    estimate   SE df t.ratio p.value
#>  mid.vs.ends   -10.56 4.47 48  -2.363  0.0222
#>  lo.vs.hi       20.00 5.16 48   3.878  0.0003
#> 
#> wool = B:
#>  contrast    estimate   SE df t.ratio p.value
#>  mid.vs.ends     5.28 4.47 48   1.182  0.2432
#>  lo.vs.hi        9.44 5.16 48   1.831  0.0733
#> 

pairs(warp.emm)
#> wool = A:
#>  contrast estimate   SE df t.ratio p.value
#>  L - M      20.556 5.16 48   3.986  0.0007
#>  L - H      20.000 5.16 48   3.878  0.0009
#>  M - H      -0.556 5.16 48  -0.108  0.9936
#> 
#> wool = B:
#>  contrast estimate   SE df t.ratio p.value
#>  L - M      -0.556 5.16 48  -0.108  0.9936
#>  L - H       9.444 5.16 48   1.831  0.1704
#>  M - H      10.000 5.16 48   1.939  0.1389
#> 
#> P value adjustment: tukey method for comparing a family of 3 estimates 

# Effects (dev from mean) of the 6 factor combs, with enhanced levels:
contrast(warp.emm, "eff", by = NULL, 
    enhance.levels = c("wool", "tension"))  
#>  contrast              estimate   SE df t.ratio p.value
#>  tensionL woolA effect  16.4074 3.33 48   4.929  0.0001
#>  tensionM woolA effect  -4.1481 3.33 48  -1.246  0.4289
#>  tensionH woolA effect  -3.5926 3.33 48  -1.079  0.4289
#>  tensionL woolB effect   0.0741 3.33 48   0.022  0.9823
#>  tensionM woolB effect   0.6296 3.33 48   0.189  0.9823
#>  tensionH woolB effect  -9.3704 3.33 48  -2.815  0.0212
#> 
#> P value adjustment: fdr method for 6 tests 
    
pairs(warp.emm, simple = "wool") # same as pairs(warp.emm, by = "tension")
#> tension = L:
#>  contrast estimate   SE df t.ratio p.value
#>  A - B       16.33 5.16 48   3.167  0.0027
#> 
#> tension = M:
#>  contrast estimate   SE df t.ratio p.value
#>  A - B       -4.78 5.16 48  -0.926  0.3589
#> 
#> tension = H:
#>  contrast estimate   SE df t.ratio p.value
#>  A - B        5.78 5.16 48   1.120  0.2682
#> 

# Do all "simple" comparisons, combined into one family
pairs(warp.emm, simple = "each", combine = TRUE)
#>  wool tension contrast estimate   SE df t.ratio p.value
#>  A    .       L - M      20.556 5.16 48   3.986  0.0021
#>  A    .       L - H      20.000 5.16 48   3.878  0.0029
#>  A    .       M - H      -0.556 5.16 48  -0.108  1.0000
#>  B    .       L - M      -0.556 5.16 48  -0.108  1.0000
#>  B    .       L - H       9.444 5.16 48   1.831  0.6594
#>  B    .       M - H      10.000 5.16 48   1.939  0.5255
#>  .    L       A - B      16.333 5.16 48   3.167  0.0241
#>  .    M       A - B      -4.778 5.16 48  -0.926  1.0000
#>  .    H       A - B       5.778 5.16 48   1.120  1.0000
#> 
#> P value adjustment: bonferroni method for 9 tests 

if (FALSE) {

## Note that the following are NOT the same:
contrast(warp.emm, simple = c("wool", "tension"))
contrast(warp.emm, simple = list("wool", "tension"))
## The first generates contrasts for combinations of wool and tension
##   (same as by = NULL)
## The second generates contrasts for wool by tension, and for 
##   tension by wool, respectively.
}

# An interaction contrast for tension:wool
tw.emm <- contrast(warp.emm, interaction = c(tension = "poly", wool = "consec"), 
                   by = NULL)
tw.emm          # see the estimates
#>  tension_poly wool_consec estimate    SE df t.ratio p.value
#>  linear       B - A           10.6  7.29 48   1.447  0.1543
#>  quadratic    B - A          -31.7 12.63 48  -2.507  0.0156
#> 
coef(tw.emm)    # see the contrast coefficients
#>   tension wool c.1 c.2
#> 1       L    A   1  -1
#> 2       M    A   0   2
#> 3       H    A  -1  -1
#> 4       L    B  -1   1
#> 5       M    B   0  -2
#> 6       H    B   1   1

# Use of scale and offset
#   an unusual use of the famous stack-loss data...
mod <- lm(Water.Temp ~ poly(stack.loss, degree = 2), data = stackloss)
(emm <- emmeans(mod, "stack.loss", at = list(stack.loss = 10 * (1:4))))
#>  stack.loss emmean    SE df lower.CL upper.CL
#>          10   18.8 0.463 18     17.9     19.8
#>          20   22.3 0.564 18     21.1     23.5
#>          30   24.9 0.646 18     23.5     26.3
#>          40   26.7 0.958 18     24.6     28.7
#> 
#> Confidence level used: 0.95 
# Convert results from Celsius to Fahrenheit:
confint(contrast(emm, "identity", scale = 9/5, offset = 32))
#>  contrast     estimate    SE df lower.CL upper.CL
#>  stack.loss10     65.9 0.833 18     64.1     67.6
#>  stack.loss20     72.1 1.015 18     70.0     74.3
#>  stack.loss30     76.8 1.163 18     74.4     79.3
#>  stack.loss40     80.0 1.724 18     76.4     83.6
#> 
#> Confidence level used: 0.95