clm function package ordinal "Hessian is numerically singular: parameters are not uniquely determined"

Question

I'm modeling ordinal data using the clm function from the ordinal package in R. For that I have 4 variables, 2 ordinal and 2 continuous (O1, O2, C1, C2).

O1 <- c(2,2,1,2,2,1,3,2,2,3,3,2,1,3,2,2,2)
O2 <- c(2,2,3,2,2,1,2,2,2,1,1,2,3,2,2,2,2)
C1 <- C(49,25,1000,19,61,700,25,375,35,46,105,437,3300,31,203,34,800)
C2 <- c(25350, 25050, 14925, 25050, 14325, 16300, 26425, 22250, 22250,
        44650, 44650, 21400, 30125, 25350, 25050, 14325, 17525)
data <- data.frame (O1, O2, C1, C2)
data <- within(data, {
O1 <- factor ((O1), ordered =TRUE,
              levels = c("1", "2", "3"))
O2 <- factor ((O2), ordered =TRUE,
              levels = c("1", "2", "3"))
})

In a first step I want to model O1 as response variable and O2, C1 and C2 as predictors (3 different models) and second, use O2 as response and O1, C1 and C2 as predictors (another 3 different models).

m1 <- clm(O1 ~ O2, data = data)
m2 <- clm(O1 ~ C1, data = data)
m3 <- clm(O1 ~ log(C2), data = data)
m4 <- clm(O2 ~ O1, data = data)
m5 <- clm(O2 ~ C1, data = data)
m6 <- clm(O2 ~ log(C2), data = data)

As you can see all models run without problem except for the first one (m1) which gives as warning message:

(1) Hessian is numerically singular: parameters are not uniquely determined In addition: Absolute convergence criterion was met, but relative criterion was not met

and do not report any standard error or wald z test.

I do not have this problem when simulating data

 data$x1 <- sample(c(1,2,3), 17, replace = TRUE)

What confuses me is that, unlike with m1 (O1 ~ O2), the model which uses O2 as response and O1 as predictor works perfectly fine. In addition I have tried replacing some values in O1 and it happened that when substituting 1 by 2 or 3 I do not get any warning message and I obtain all the coefficients of the model.

I made some research and it seems and this can be due to low representation of certain values in the response, as well as to a small sample size. Is that right or can it be a bug? Can someone help me please?

Answer 1

It is because you have too many empty cells (here you have only 2 subjects iwith O2=3) Try to merge categories and refit the model