# Re: [R] glm-logistic on discrete-time methods with individual and aggregated data

From: Spencer Graves <spencer.graves_at_pdf.com>
Date: Mon 06 Feb 2006 - 09:02:56 EST

You've found a region of infinite extent over which the likelihood function is for all practical purposes flat. This means that the maximum likelihood estimates (MLEs) are not unique. To see this consider the following properties of your datiINDa:

> with(datiINDa, table(statusINDa, timesINDa))

timesINDa
statusINDa 1 2 3 4

```          0 10  8  6  4
1  0  2  2  2
```

> sapply(datiINDa, class)
timesINDa statusINDa
"factor" "numeric"

You are estimating 4 parameters, an intercept plus one parameter for each level of the factor "timesInda". The first level occurs only with statusINDa = 0, never with statusINDa = 1. Therefore, the theoretical MLE for that level of timesINDa would have slope = +/-Inf (and the intercept would also be adjusted to +/-Inf to compensate). However, glm doesn't bother pushing it that far, and gives up with still moderately small values for the parameters. To understand this better, first modify your example to store the glm fitted object as follows:

fit.a <- glm(statusINDa ~ timesINDa, family=binomial, data=datiINDa)

Then apply "predict" to that object:

predict(fit.a, type="response")

The result is that the 10 cases with timesInda = 1 all have a Pr{statusINDa = 1} = 3e-9, which glm thinks is essentially 0 and quits.

Now let's do the same with your weighted version:

fit.wa <- glm(statusAGGa ~ timesAGGa, family=binomial, data=datiAGGa, weights=weightAGGa)
sort(predict(fit.wa, type="response"))

Those 10 cases now have Pr{statusINDa = 1} = 5.4e-9. This is essentially the issue of "complete separation". We can request more precision as follows:

> fit.a3 <- glm(statusINDa ~ timesINDa, family=binomial, data=datiINDa,

```+           control=glm.control(epsilon=1e-13,
+             maxit=250))
```

Warning message:
fitted probabilities numerically 0 or 1 occurred in: glm.fit(x = X, y = Y, weights = weights, start = start, etastart = etastart,

In this case, we get a warning. For more on this, try RSiteSearch("complete separation with logistic regression").

```	  Sehr interessant, nicht?
hope this helps.
spencer graves

```

Camarda, Carlo Giovanni wrote:

> Dear R-Users,
> without going into details I tried to prepare a simple example to show
> you where I would need help.
> In particular I prepare two examples-template for a study I'm conduction
> on discrete-time methods for survival analysis.
> Each of this example has two datasets which are basically equal, with
> the exception that in the former one has individual data and in the
> latter one aggregated data.
> The difference between the two examples is on a single subject: I
> substituted to the first example a censored case with a subject who died
> at the first time-unit.
> Afterward I fitted a logistic model (Fahrmeir and Tutz, 2001) in the glm
> context, but whereas there is not difference between individual and
> aggregated dataset in the first example, I noted some discrepancies in
> the second example. I might guess that something with weights is going
> on, but I did not manage to clearly understand.
> Hope that the following example will be more clear than my explanations,
> Carlo Giovanni Camarda
>
>
> rm(list = ls())
> # working one
>
> timesIND <- c(rep(1:4, 3), 1, rep(1:2,2), rep(1:3 , 2), rep(1:4,
> 2))
> statusIND <- c(rep(0 ,12), 1, rep(0:1,2), rep(c(0,0,1), 2),
> rep(c(0,0,0,1),2))
> datiIND <- as.data.frame(cbind(timesIND, statusIND))
> datiIND\$timesIND <- as.factor(datiIND\$timesIND)
>
> timesAGG <- c( 1:4, 1, 1:2, 1:3, 1:4)
> statusAGG <- c(rep(0,4), 1, 0:1, c(0,0,1), c(0,0,0,1))
> weightAGG <- c(rep(3,4), 1, rep(2,2), rep(2,3), rep(2,4))
> datiAGG <- as.data.frame(cbind(timesAGG, statusAGG, weightAGG))
> datiAGG\$timesAGG <- as.factor(datiAGG\$timesAGG)
>
> coef(glm(statusIND ~ timesIND, family=binomial, data=datiIND))
> coef(glm(statusAGG ~ timesAGG, family=binomial, data=datiAGG,
> weights=weightAGG))
>
> # not working one
>
> timesINDa <- c(rep(1:4, 4), rep(1:2,2), rep(1:3 , 2), rep(1:4,
> 2))
> statusINDa <- c(rep(0 ,16), rep(0:1,2), rep(c(0,0,1), 2),
> rep(c(0,0,0,1),2))
> datiINDa <- as.data.frame(cbind(timesINDa, statusINDa))
> datiINDa\$timesINDa <- as.factor(datiINDa\$timesINDa)
>
> timesAGGa <- c( 1:4, 1:2, 1:3, 1:4)
> statusAGGa <- c(rep(0,4), 0:1, c(0,0,1), c(0,0,0,1))
> weightAGGa <- c(rep(4,4), rep(2,2), rep(2,3), rep(2,4))
> datiAGGa <- as.data.frame(cbind(timesAGGa, statusAGGa, weightAGGa))
> datiAGGa\$timesAGGa <- as.factor(datiAGGa\$timesAGGa)
>
> coef(glm(statusINDa ~ timesINDa, family=binomial, data=datiINDa))
> coef(glm(statusAGGa ~ timesAGGa, family=binomial, data=datiAGGa,
> weights=weightAGGa))
>
> +++++
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>
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