"normal" for normal distribution, "t-dist" for t-distribution.
df
Degrees of freedom (for t-distribution).
.rse
Residual standard error.
.alpha
Significance level.
mean
Causal estimate.
se
Standard error of estimate.
Details
The slight complication of this function is that when the estimate of the residual standard error (RSE) is less than one, the t-distribution confidence interval is calculated as either the confidence interval using a normal deviate and setting the RSE to 1, or a t-distribution deviate and using the estimated RSE. The wider of the two intervals is reported. This ensures that under-dispersion is not doubly penalized, while also making sure that the estimate is no more precise than that from a fixed-effect analysis.