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log: C:\AAA Miker Files\newer web pages\soc_388_notes\soc_388_2007\third_class_notes.lo
> g
log type: text
opened on: 2 Oct 2007, 11:03:04
. set linesize 75
. *We have talked a bit about likelihood ratio tests and comparing models,
> now let's look at the output from Stata and see what that looks like.
. use "C:\AAA Miker Files\newer web pages\soc_388_notes\soc_388_2007\frogs. dta", clear
. *frogs dataset
. *first, let's look at the indepdence model.
. desmat: poisson count color live
---------------------------------------------------------------------------
Poisson regression
---------------------------------------------------------------------------
Dependent variable count
Optimization: ml
Number of observations: 4
Initial log likelihood: -14.328
Log likelihood: -9.540
LR chi square: 9.578
Model degrees of freedom: 2
Pseudo R-squared: 0.334
Prob: 0.008
---------------------------------------------------------------------------
nr Effect Coeff s.e.
---------------------------------------------------------------------------
count
color
1 Green -0.693** 0.245
live
2 Water 0.241 0.233
3 _cons 3.091** 0.192
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* p < .05
** p < .01
. *at the top of every poisson regression, we get a LRT statistic that compares to the constant only model, which is usually not very interesting because the constant only model is usually rather stupid.
. *For this test between the indepdence model and the constant only model, we get a statistic of 9.578 on 2df, which rejects the constant only model but not dramatically.
. display chi2tail(2,9.578)
.00832077
. *The answer is a little less than 1 percent. So we are reasonably sure that the constant only model doesn't fit the data, but given that the number of frogs is not that great, and the distribution across the 4 cells was not dramatically skewed, there is a remote chance (1 in 100 or so) that a constant only distribution (with random variation) could yield as much deviation from evenness as we saw in this frog dataset.
. *The more interesting test is the comparison to the saturated model, or the actual data, and that we get by adding commands after we run the poisson regression. This comparison requires the “poisgof” command after we run the poisson regression.
. poisgof
Goodness-of-fit chi2 = .2445188
Prob > chi2(1) = 0.6210
. poisgof, pearson
Goodness-of-fit chi2 = .2435065
Prob > chi2(1) = 0.6217
. *because the statistic here is smaller than 1 on 1df, the p value is greater than .5, meaning we cannot reject that the data actually came from the independence distribution.
. *Another way of saying this is that if the data were generated from an independence model, we would expect this much deviation from independence 62% of the time, which is a lot.
. *This is another way of saying that there doesn't seem to be a significant interaction between frog color and where the frog lives, which we tested a different way by looking at the odds ratio of interaction, which was also insignificant.
.
. *That is the basic start.
. *One thing to keep straight in Stata is the difference between tabulate and table.
. *Both can give you frequency cross-tabulations
. *Table can actually put any statistic you like in the table, whereas tabulate can give you fit statistics
. tabulate color live [fweight=count], lrchi2 chi2
| live
Color | Lilly Water | Total
-----------+----------------------+----------
Blue | 23 27 | 50
Green | 10 15 | 25
-----------+----------------------+----------
Total | 33 42 | 75
Pearson chi2(1) = 0.2435 Pr = 0.622
likelihood-ratio chi2(1) = 0.2445 Pr = 0.621
. *You don't need to run a log linear model to calculate the chisquare statistic for goodness of fit. In fact, Tabulate in Stata and any frequency table program will generate these statistics for you. Note that the goodness of fit tests were exactly what we got from poisgof after our independence model.
. desmat: poisson count color live, verbose
Desmat generated the following design matrix:
nr Variables Term Parameterization
First Last
1 _x_1 color ind(1)
2 _x_2 live ind(1)
Iteration 0: log likelihood = -9.5395876
Iteration 1: log likelihood = -9.5395873
Poisson regression Number of obs =
> 4
LR chi2(2) = 9.
> 58
Prob > chi2 = 0.00
> 83
Log likelihood = -9.5395873 Pseudo R2 = 0.33
> 42
----------------------------------------------------------------------------
> --
count | Coef. Std. Err. z P>|z| [95% Conf. Interva
> l]
-------------+--------------------------------------------------------------
> --
_x_1 | -.6931472 .244949 -2.83 0.005 -1.173238 -.2130
> 56
_x_2 | .2411621 .2326211 1.04 0.300 -.2147668 .69709
> 09
_cons | 3.091042 .1922751 16.08 0.000 2.71419 3.4678
> 95
----------------------------------------------------------------------------
> --
----------------------------------------------------------------------------
Poisson regression
----------------------------------------------------------------------------
Dependent variable count
Optimization: ml
Number of observations: 4
Initial log likelihood: -14.328
Log likelihood: -9.540
LR chi square: 9.578
Model degrees of freedom: 2
Pseudo R-squared: 0.334
Prob: 0.008
----------------------------------------------------------------------------
nr Effect Coeff s.e.
----------------------------------------------------------------------------
count
color
1 Green -0.693** 0.245
live
2 Water 0.241 0.233
3 _cons 3.091** 0.192
----------------------------------------------------------------------------
* p < .05
** p < .01
* Verbose option after desmat shows us the creation of the dummy variables, and how many steps it takes the software to find the set of parameters that maximize the likelihood. In this case, because it is an easy model, it took only one step. But big datasets with sparse data can take thousands of steps or can fail to converge altogether.
. *in the department of learning stata, table can do some nice things with Table.
. table color live, contents(mean _x_1)
------------------------
| live
Color | Lilly Water
----------+-------------
Blue | 0 0
Green | 1 1
------------------------
. *in this case showing us what the dummy variable for color looks like.
. exit, clear