Model for dataset with a very small number of incidents.

[Luis Mijares Castaneda]

Hello, I was wondering if anyone could provide advice on model selection for my dataset. I have data from a longitudinal survey with five waves: one baseline wave and four follow-up waves. My goal is to model post-baseline home eviction rates.

The challenge is that only 18 participants reported experiencing at least one home eviction during follow-up. I use the number of home evictions as the outcome variable and the total number of post-baseline waves completed as the exposure (offset) in a Poisson regression model, along with the covariates listed below.

My concern is that the number of non-zero outcomes is so small that the model appears to be overfit, resulting in very wide confidence intervals. Could anyone recommend an alternative modeling approach for count data with such a small number of events, or suggest strategies for handling this type of sparse outcome?




c.ppage ///
i.biosex ///
i.race_alt ///
i.education ///
i.region ///
i.income ///
i.Personal_debt ///
c.sf8pcs ///
c.sf8mcs ///
i.asud ///
i.asmi ///
i.housetype_alt ///
i.employment, ///
exposure(total_years) ///

 tab total_years

  Number of |
      waves |
 present in |
 the survey |      Freq.     Percent        Cum.
------------+-----------------------------------
          1 |         91       10.87       10.87
          2 |        110       13.14       24.01
          3 |        113       13.50       37.51
          4 |        523       62.49      100.00
------------+-----------------------------------
      Total |        837      100.00

. tab any_eviction_count

      Total |
  number of |
  evictions |
       from |
Year01-Year |
         04 |      Freq.     Percent        Cum.
------------+-----------------------------------
          0 |        819       97.85       97.85
          1 |         13        1.55       99.40
          2 |          1        0.12       99.52
          3 |          2        0.24       99.76
          4 |          2        0.24      100.00
------------+-----------------------------------
      Total |        837      100.00

[Felix Bittmann]

Given your very low number of events I think there is no work to produce any reliable results. Even a single explanatory variable might not work... You need to find richer data first.

[John Mullahy]

In principle Poisson models are no less valid when Prob(y=0) is very large (e.g. .98) than when it is smaller.

Short of obtaining new data two possible strategies to consider are:

1. Model as longitudinal Poisson with appropriate robust standard errors.

2. Model the binary outcome 1(y>0) using logit or probit.