Fits multinomial regression model $$ P_i = \frac{ \exp( X^\beta_i ) }{ \sum_{j=1}^K \exp( X^\beta_j ) }$$ for $$i=1,..,K$$ where $$\beta_1 = 0$$, such that $$\sum_j P_j = 1$$ using phreg function. Thefore the ratio $$\frac{P_i}{P_1} = \exp( X^\beta_i )$$
mlogit(formula, data, offset = NULL, weights = NULL, fix.X = FALSE, ...)formula with outcome (see coxph)
data frame
offsets for partial likelihood
for score equations
to have same coefficients for all categories
Additional arguments to lower level funtions
Coefficients give log-Relative-Risk relative to baseline group (first level of factor, so that it can reset by relevel command). Standard errors computed based on sandwhich form $$ DU^-1 \sum U_i^2 DU^-1$$.
Can also get influence functions (possibly robust) via iid() function, response should be a factor.
Can fit cumulative odds model as a special case of interval.logitsurv.discrete
data(bmt)
dfactor(bmt) <- cause1f~cause
drelevel(bmt,ref=3) <- cause3f~cause
dlevels(bmt)
#> cause1f #levels=:3
#> [1] "0" "1" "2"
#> -----------------------------------------
#> cause3f #levels=:3
#> [1] "2" "0" "1"
#> -----------------------------------------
mreg <- mlogit(cause1f~+1,bmt)
summary(mreg)
#>
#> n events
#> 1224 408
#>
#> 1224 clusters
#> coeffients:
#> Estimate S.E. dU^-1/2 P-value
#> XX(Intercept).2 0.0062305 0.1116297 0.1116297 0.9555
#> XX(Intercept).3 -0.6092657 0.1332076 0.1332076 0.0000
#>
#> exp(coeffients):
#> Estimate 2.5% 97.5%
#> XX(Intercept).2 1.00625 0.80851 1.2523
#> XX(Intercept).3 0.54375 0.41881 0.7060
#>
#>
mreg <- mlogit(cause1f~tcell+platelet,bmt)
summary(mreg)
#>
#> n events
#> 1224 408
#>
#> 1224 clusters
#> coeffients:
#> Estimate S.E. dU^-1/2 P-value
#> XX(Intercept).2 0.25002 0.13906 0.13858 0.0722
#> XXtcell.2 -0.28389 0.36431 0.36285 0.4358
#> XXplatelet.2 -0.68611 0.24797 0.24956 0.0057
#> XX(Intercept).3 -0.56565 0.16921 0.17078 0.0008
#> XXtcell.3 0.50505 0.36481 0.36226 0.1662
#> XXplatelet.3 -0.35890 0.29130 0.28727 0.2179
#>
#> exp(coeffients):
#> Estimate 2.5% 97.5%
#> XX(Intercept).2 1.28406 0.97773 1.6864
#> XXtcell.2 0.75285 0.36864 1.5375
#> XXplatelet.2 0.50353 0.30971 0.8187
#> XX(Intercept).3 0.56799 0.40767 0.7914
#> XXtcell.3 1.65707 0.81062 3.3874
#> XXplatelet.3 0.69844 0.39462 1.2362
#>
#>
mreg3 <- mlogit(cause3f~tcell+platelet,bmt)
summary(mreg3)
#>
#> n events
#> 1224 408
#>
#> 1224 clusters
#> coeffients:
#> Estimate S.E. dU^-1/2 P-value
#> XX(Intercept).2 0.56565 0.16921 0.17078 0.0008
#> XXtcell.2 -0.50505 0.36481 0.36226 0.1662
#> XXplatelet.2 0.35890 0.29130 0.28727 0.2179
#> XX(Intercept).3 0.81567 0.16346 0.16467 0.0000
#> XXtcell.3 -0.78894 0.39244 0.38890 0.0444
#> XXplatelet.3 -0.32721 0.30423 0.30139 0.2821
#>
#> exp(coeffients):
#> Estimate 2.5% 97.5%
#> XX(Intercept).2 1.76059 1.26364 2.4530
#> XXtcell.2 0.60347 0.29521 1.2336
#> XXplatelet.2 1.43175 0.80893 2.5341
#> XX(Intercept).3 2.26070 1.64100 3.1144
#> XXtcell.3 0.45433 0.21053 0.9804
#> XXplatelet.3 0.72093 0.39713 1.3087
#>
#>
## inverse information standard errors
lava::estimate(coef=mreg3$coef,vcov=mreg3$II)
#> Estimate Std.Err 2.5% 97.5% P-value
#> XX(Intercept).2 0.5657 0.1708 0.2309 0.90038 9.259e-04
#> XXtcell.2 -0.5051 0.3623 -1.2151 0.20497 1.633e-01
#> XXplatelet.2 0.3589 0.2873 -0.2041 0.92194 2.115e-01
#> XX(Intercept).3 0.8157 0.1647 0.4929 1.13842 7.294e-07
#> XXtcell.3 -0.7889 0.3889 -1.5512 -0.02672 4.249e-02
#> XXplatelet.3 -0.3272 0.3014 -0.9179 0.26350 2.776e-01
## predictions based on seen response or not
newdata <- data.frame(tcell=c(1,1,1),platelet=c(0,1,1),cause1f=c("2","1","0"))
predictmlogit(mreg,newdata,response=FALSE)
#> 0 1 2
#> 1 0.3438904 0.3324396 0.3236700
#> 2 0.4663875 0.2270204 0.3065921
#> 3 0.4663875 0.2270204 0.3065921
predictmlogit(mreg,newdata)
#> pred se lower upper
#> 1 0.3236700 0.13603308 0.05705011 0.5902900
#> 2 0.2270204 0.12225406 -0.01259315 0.4666340
#> 3 0.4663875 0.07376361 0.32181348 0.6109615