ppm: Fitting a Proportional Probability Model

In lcpm: Ordinal Outcomes: Generalized Linear Models with the Log Link

Description

ppm provides the maximum likelihood estimate for ordinal outcomes (J>2 categories) and a Generalized Linear Model with the log link with the assumption of proportionality. That is, ppm determines the MLE for log[P(y <= j)]= cut_j + X beta subject to [cut_j-1 <= cut_j ] and [cut_j + X beta <=0]. This implementation uses constrOptim to determine the MLE and so the results should correctly account for the restricted parameter space. A proposed test for proportionality is included in lcpm.

Usage

ppm(
  formula.linear,
  data,
  conf.level = 0.95,
  y.order = NULL,
  startval = NULL,
  less.than.0 = TRUE,
  control.list = NULL,
  eps.outer = NULL,
  ...
)

Arguments

formula.linear	an object of class "formula": a symbolic description of the linear model to be fitted.
data	dataframe containing the data in linear model.
conf.level	optional confidence level (1-alpha) defaulted to 0.95.
y.order	optional if y contains ordered integer categories 1:J. If y is not ordered integer 1:J then this is a vector with the ordinal values for y ranging from the lowest to largest ordinal outcome. See Examples below.
startval	optional vector of the starting values.
less.than.0	optional logical for constraint cut_j <= 0 for all j=1:(J-1). Default is TRUE.
control.list	optional list of controls for constrOptim.
eps.outer	option for constrOptim.
...	Additional arguments for built in functions.

Value

list of class "ppm" is returned containing:

coefficients	vector of the estimate of cut_j and beta
se	vector of the estimate of standard errors
vcov	matrix of the inverse of the negative Hessian
fitted.values	matrix of unique covariates and the corresponding estimate of the cumulative probabilities: exp(X %*% coefficients)
loglik	numerical value of the log-likelihood at the maximum likelihood estimate
barrier.value	value of mu in the log-barrier algorithm
outer.iterations	value of the number of outer iterations
formula	formula in the call of ppm
startvalues	vector of the starting values for constrained optimization algorithm

Note

A warning of MLE close to the boundary must be carefully considered. Data may have some structure that requires attention. Additionally, there is no imputation. Any NA results in complete row removal.

References

Singh, G; Fick, G.H. (accepted) Ordinal outcomes: a cumulative probability model with the log link and an assumption of proportionality. Statistics in Medicine.

See Also

lcpm

Examples

# 2 examples below showing the use of y.order if outcome are not integers 1:J.

# Example 1:

var_a <- c(rep(0,60),rep(1,60))
var_b <- c(rep(0,90),rep(1,30))
y1<-c(rep(2,5),rep(3,10),rep(5,5),rep(10,10),
rep(2,5),rep(3,10),rep(5,10),rep(10,5),
rep(2,10),rep(3,5),rep(5,5),rep(10,10),
rep(2,10),rep(3,5),rep(5,10),rep(10,5))

testdata<-data.frame(y=y1,var_a=var_a,var_b=var_b)

# PPM estimates for proportional model
test1<-ppm( y ~ var_a + var_b, data=testdata, y.order=c(2,3,5,10))
summary(test1)

# Example 2:

y2<-c(rep("a",5),rep("b",10),rep("c",5),rep("d",10),
rep("a",5),rep("b",10),rep("c",10),rep("d",5),
rep("a",10),rep("b",5),rep("c",5),rep("d",10),
rep("a",10),rep("b",5),rep("c",10),rep("d",5))
testdata2<-data.frame(y=y2,var_a=var_a,var_b=var_b)
test2<-ppm(y~var_a + var_b , data=testdata2, y.order=c("a","b","c","d"))
summary(test2)

lcpm documentation built on Jan. 9, 2020, 9:07 a.m.