Dear every experts in statistics：
Given I have three variables (die,x1, x2). These variables are all dichotomous and every variables have six values. Data list in following :
die x1 x2
0 0 1
0 0 0
0 0 1
1 0 0
1 1 1
1 1 1
I do logistc regression in STATA as following:
logit die x1
The results is following:
note: x1 != 0 predicts success perfectly
x1 dropped and 2 obs not used
Logistic regression Number of obs = 4
LR chi2(0) = 0.00
Prob > chi2 = .
Log likelihood = -2.2493406 Pseudo R2 = 0.0000
------------------------------------------------------------------------------
die | Odds Ratio Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
x1 | 1 (omitted)
_cons | .3333333 .3849002 -0.95 0.341 .0346734 3.20451
------------------------------------------------------------------------------
I find the Odds Ratio for x1 is 1 and number in this regression is four
My question is why the number change from 6 to 4 ?
logistic die x2
The results is following:
Logistic regression Number of obs = 6
LR chi2(1) = 0.68
Prob > chi2 = 0.4097
Log likelihood = -3.819085 Pseudo R2 = 0.0817
------------------------------------------------------------------------------
die | Odds Ratio Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
x2 | 4 6.928203 0.80 0.423 .1341948 119.2297
_cons | .5 .6123724 -0.57 0.571 .0453383 5.514101
------------------------------------------------------------------------------
I find the Odds Ratio for x2 is 4 and number in this regression is six
Then i do mutiple logistic regress in STATA
logistic die x1 x2
The results is following:
note: x1 != 0 predicts success perfectly
x1 dropped and 2 obs not used
note: x2 != 0 predicts failure perfectly
x2 dropped and 1 obs not used
Logistic regression Number of obs = 3
LR chi2(0) = 0.00
Prob > chi2 = .
Log likelihood = -1.9095425 Pseudo R2 = 0.0000
------------------------------------------------------------------------------
die | Odds Ratio Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
x1 | 1 (omitted)
x2 | 1 (omitted)
_cons | .5 .6123724 -0.57 0.571 .0453383 5.514101
------------------------------------------------------------------------------
I find the Odds Ratio for x2 change to 1 and number in this regression is three
Why this happen? What should i do?
Thanks very much!
Wandong Hong
This is about confounding when a new variable enters into equation odds ratios and coefficients change because your model changes.
Dear Ph D Iyisoy
Thanks for your answer. I still confused that should i remove the X1 when i do multiple logistic regression?
Wandong Hong
Check the VIF for your independent variables. If its greater than 10 then multi-collinearity may exist.
What is your aim? Are you trying to form a model? Why do you want to remove/include x1?
Prematurely I can say no you should keep it. But your answer to my questions are important.
Thanks Pandey for your answer
Like in this case, the VIF is all small than 10
Collinearity Diagnostics
SQRT R-
Variable VIF VIF Tolerance Squared
----------------------------------------------------
x1 2.00 1.41 0.5000 0.5000
x2 2.00 1.41 0.5000 0.5000
----------------------------------------------------
Mean VIF 2.00
Cond
Eigenval Index
---------------------------------
1 2.4051 1.0000
2 0.4359 2.3491
3 0.1590 3.8895
---------------------------------
Condition Number 3.8895
Eigenvalues & Cond Index computed from scaled raw sscp (w/ intercept)
Det(correlation matrix) 0.5000
Thanks Ph D Iyisoy for your answer
YES , I am try to form a model. assume x2 must be adjusting x1. Then what i shoud do ?
Thanks for your answer. I find the Odds Ratio for x2 change to 1 and number in this regression is reduced to four if I include both, which means the model become insignifcanct and I would miss two values for all variable
Model will never be insignificant. If you believe that both x1 and x2 should be in the model, then you should include them regardless of their statistical significance.
By the way, I should mention that 6 observations is too small for making inferences.
I think the problem is not so much related to multicollinearity or confounding, but to lack of sufficient information in a small data set. (I agree with Iyisoy that the data set with 6 observations is too small.)
The problem is that the group defined by x1=1 only contains values die=1 and not cases with die=0. Therefore, the proportion of die=1 in this group equals 1 and thus the odds equals 1 / 0 = inf. This means that the parameter for this group in the logistic regression model cannot be estimated, as the log-odds are also inf. in this group.
Because you have dummy variables as predictors, the logistic model can easily be computed by hand, just by calculating the propotions die=1 in the groups, and with these the log-odds and then writing the model down. This shows your problem. STATA probably removed the two cases with x1=1 to be able to estimate a model? (I'm not sure but you can easily check this this by close inspection of the output.) I ran an SPSS analysis, which actually gives an estimate for all 6 cases, but with very large SE's and extremely large odds-ratios, showing that the information to come up with good estimates is lacking (as was expected).
Mark, actually I did not pay attention to data too much (thanks for pointing out the issue). I assumed those 6 and 4's to be parameter estimates from his words, but I see now that those were number of observations included in the models. I do not have Stata available right now, so I can not replicate the analysis.
I guess the problem is with quasi-complete separation. Here x1 quasi-completely separates the outcome variable and I guess Stata removes those two observations of x1=1 to remedy.
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