Suppose that we fit a model to a response variable that has been transformed using some function g as above, and obtain an estimate of a mean L в ■ Pro­grams including SAS will also output an estimate of the variance of L в ■ We can compute the estimate of the mean in the original scale by applying the inverse transformation g-1 to Lв as described above. In order to obtain an estimate of the variance of g-1 (L в), however, we need to make use of, for example, the Delta method, which we now explain.   Given any non-linear function H of some scalar-valued random variable в, И(в) and given s2, the variance of в, we can obtain an expression for the variance of И(в) as follows:

For example, suppose that we used a log transformation on a response variable and obtained an LSM in the transformed scale that we denote L в, with estimated variance <OL■ The estimate of the mean in the original scale is obtained by apply­ing the inverse transformation to the LSM:

m = LSM.. = exp (L в)

original   The variance of m is given by:

Suppose now that the response variable was binary and that we used a logit transformation so that

Given an MLE в and an estimate of L в the least squares mean in the trans­formed scale, we compute m and &m as follows:  exp ( l в)

1 + exp (L в)

Г 2 = exP (L ‘P) Г

m |^1 + exp( L’P) ів

Given a point estimate of the least squares mean in the original scale and an approximation to its variance, we can compute an approximate 100(1-a)% con­fidence interval for the true mean in the original scale in the usual manner:

100(1- a)% for m = m ± tdfa,2Г,

where df is the appropriate degrees of freedom. In our case, and due to relatively large sample sizes everywhere, the t critical value can be replaced by the corre­sponding upper al2 tail of the standard normal distribution.

Main Considerations for Taking a Position by Number of Respondents Saying

“Yes”

 Consideration Gender of Respondent Male Female Pay 90 88 Benefits 65 62 Promotion opportunities 101 91 Start-up package 131 117 Funding opportunities 96 100 Family-related reasons 120 168 Job location 156 176 Collegiality 170 209 Reputation of department or university 184 224 Quality of research facilities 152 155 Access to research facilities 130 134 Opportunities for research collaboration 179 216 Desire to build or lead a new program or area of research 165 152 This was the only offer I received 52 48
 NOTE: There were a total of 612 males and 666 females that responded in each category.