# Why am I getting a zero parameter estimate and SE for one of my variables in a logistic regression?

I am doing a binary logit analysis, in which I'm trying to fit a model to my data to explain why some towns adopt open space subdivision ordinances (OP), using a handful of discrete and continuous independent variables. One of the explanatory variables, median household income, is coming back with an estimated beta of 0, with a S.E. of 0, and a p value of (0.14), and the Odds Ratio is 1 (S.E. of 0). It is highly unlikely that there is absolutely no relation between household income and towns passing a growth management ordinance, so this seems pretty odd. The rest of my variables have normal looking estimates and errors. This is my first time asking a question on this site, so please forgive me if I leave out critical information - I'll explain more if needed. I tried to cut and paste my output below, but the formatting of the table disappeared, making it impossible to decipher.

Also, my descriptive statistics for household income look fine, with realistic minimum, maximum and mean numbers, and the original data doesn't show anything obviously wrong with the data itself, which makes me think I'm doing something wrong when estimating my model.

On a side note, my odds ratio results for percent change in housing from 1990-2000 (PCHU90_00) look really high, and well, odd =) I'm not sure what's going on there, either.

Any suggestions would be appreciated. Thank you!

Here's the model:

LOGIT
MODEL OP = CONSTANT+COAST+LA_SQMI+PCHU00_10+PCHU70_80+PCHU80_90+PCHU90_00+CONSTEMP+
HHINCOME+LT+PCHPOP00_10+PCHPOP60_70+PCHPOP70_80+PCHPOP80_90+PCHPOP90_00+PCTDEM


And the results for the two variables I'm concerned about:

HHINCOME: 0 Beta (0 SE), z=1.46, p=0.14, 1.0 Odds Ratio (0 SE)
PCHU90_00: 9.64 (3.89 SE), z=2.47, p=.01, 15310.11 Odds Ratio (59625.59 SE)


Model fit info seems okay -

Log-Likelihood of Constants only Model = LL(0):-83.14
2*[LL(N)-LL(0)] :37.13
df:15
p-value:0.00
McFadden's Rho-squared  0.22
Cox and Snell R-square  0.25
Naglekerke's R-square   0.35

• Are you able to post your data? – Max Oct 25 '12 at 22:56
• Because I'm new, I can't attach anything to my posts =( I'm assuming you mean the excel worskheet? I can cut and paste the SYSTAT output, but it loses its formatting. Would that be helpful, though? – vanessa Oct 25 '12 at 23:04
• For PCHU90_00, it is possible that this variable is highly correlated with one or more of the other predictors. Since they are panel variables in different years, it's possible. Try run a correlation matrix using all the PCHUxx_xx variables and see if you can identify any culprit. I'm not familiar with SYSTAT, but if you have learned VIF and/or tolerance in linear regression, run the model in linear regression (It's okay, the outcome does not matter here) and check the VIF or tolerance for possible collinearity. – Penguin_Knight Oct 26 '12 at 0:02
• I see that you get a log(OR) of 0 and a SE of 0, but still z is computed. Could it be that, due to the unit of measurement of the HHINCOME variable, your point estimate is so tiny that the software rounds it and displays it as a 0? Try to change the unit of measurement (e.g. generate a new variable =HHINCOME/1000 or something like that) and see what happens. @vanessa – boscovich Oct 26 '12 at 7:40
• @andrea - BINGO! I just changed my output to be displayed to 6 decimal points, and sure enough, the estimate for HHINCOME is now 0.000068, with a standard error of 0.000028. Seems really obvious now, and I thank you for pointing this out to me. – vanessa Oct 26 '12 at 14:24