se_comb | R Documentation |

This function uses the Delta method to calculate standard errors of linear
functions of variables (similar to `lincom`

in Stata). Generally, users will not need to
call this function directly.

```
se_comb(expnms, covmat, grad = NULL)
```

`expnms` |
a character vector with the names of the columns to be of interest in the covariance matrix for a which a standard error will be calculated (e.g. same as expnms in qgcomp fit) |

`covmat` |
covariance matrix for parameters, e.g. from a model or bootstrap procedure |

`grad` |
the "weight" vector for calculating the contribution of each variable in expnms to the final standard error. For a linear combination, this is equal to a vector of ones (and is set automatically). Or can be calculated via the grad.poly procedure, in the case of coming up with proper weights when the combination of expnms derives from a polynomial function (as in qgcomp.glm.boot with degree>1). |

This function takes inputs of a set of exposure names (character vector)
and a covariance matrix (with colnames/rownames that contain the full set
of exposure names), as well as a possible `grad`

parameter to calculate
the variance of a weighted combination of the exposures in `expnms`

, where the
weights are based off of `grad`

(which defaults to 1, so that this function
yields the variance of a sum of all variables in `expnms`

)

Here is simple version of the delta method for a linear combination of three model coefficients:

`f(\beta) = \beta_1 + \beta_2 + \beta_3`

given gradient vector

```
G = [d(f(\beta))/d\beta_1 = 1,
d(f(\beta))/d\beta_2 = 1,
d(f(\beta))/d\beta_3 = 1]
```

`t(G) Cov(\beta) G`

= delta method variance, where t() is the transpose operator

```
vcov = rbind(c(1.2, .9),c(.9, 2.0))
colnames(vcov) <- rownames(vcov) <- expnms <- c("x1", "x2")
se_comb(expnms, vcov, c(1, 0))^2 # returns the given variance
se_comb(expnms, vcov, c(1, 1)) # default linear MSM fit: all exposures
# have equal weight
se_comb(expnms, vcov, c(.3, .1)) # used when one exposure contributes
# to the overall fit more than others = d(msmeffect)/dx
```

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