Marginal effects from estat mfx after asclogit - stata

Question

I am trying to understand how Stata calculates both the probability that an alternative is selected and the marginal effect calculated that the mean when I estat mfx after estimating a McFadden / conditional logit model using asclogit.
For example:
asclogit H t, case(ID) alternatives(AQ) casevars(Medicaid) ///
basealternative(1) vce(cluster Medicaid)
estat mfx, varlist(Medicaid)
My goal is to re-create the results by estimating the same model using the clogit and manually calculating the equivalent marginal effects. I am able to reproduce the conditional logit estimates generated by asclogit using clogit but I get stuck reproducing the post estimation calculations.
I have not been able to re-produce computed probability of each alternative being selected, which from reading the documentation for estat mfx I learned is evaluated at the value that is labeled X in the table output.
Here are the estat probability figures:
In case the picture didn't come out:
. matrix baseline = r(pr_1)\r(pr_2)\r(pr_3)\r(pr_4)\r(pr_5)
. matrix list baseline
baseline[5,1]
c1
r1 .04077232
r2 .15206384
r3 .01232535
r4 .10465885
r5 .69017964
Keep in mind that the variables beginning with Valpha and VMedicaid are case specific variables I created for the clogit command. They are respectively the intercept and an indicator for Medicaid coverage.
Here is what I have:
clogit H t Valpha* i.VMedicaid_2 i.VMedicaid_3 i.VMedicaid_4 i.VMedicaid_5 , ///
group(ID) vce(cluster Medicaid)
* Reproducing probability an alternative selected calculated by estat mfx
// calculate covariate means to plug into probability calculations
local V t Valpha* VMedicaid_* Medicaid
foreach var of varlist `V' {
summarize `var'
scalar `var'_MN = r(mean)
}
// alternative specific ZB
scalar zb = _b[t]*t_MN
// numerators attempt 1
foreach j of numlist 2/5 {
scalar XB`j' = exp(zb + (_b[Valpha_`j']*Valpha_`j'_MN) + ///
(_b[1.VMedicaid_`j']*VMedicaid_`j'_MN))
di "this is `j': " XB`j'
}
// numerators attempt 2, documentation for estat mfx said that probably was
// evaluated with Medicaid= 0.68 which is the Medicaid coverage rate across cases
// rather than the mean of the various VMedicaid_ variables are used to estimate
// clogit. Replaced intercept mean with 1
foreach j of numlist 2/5 {
scalar XB`j' = exp(zb + (_b[Valpha_`j']) + (_b[1.VMedicaid_`j' *Medicaid_MN))
di "this is `j': " XB`j'
}
scalar XB1 =exp(zb)
// denominator
scalar DNM = XB1+ XB2+ XB3+ XB4 + XB5
// Baseline
foreach j of numlist 1/5 {
scalar PRB`j' = XB`j'/DNM
di "The probability of choosing hospital `j' is: " PRB`j'
}
The results I get are the following:
The probability of choosing hospital 1 is: .14799075
The probability of choosing hospital 2 is: .21019437
The probability of choosing hospital 3 is: .09046377
The probability of choosing hospital 4 is: .18383085
The probability of choosing hospital 5 is: .36752026