GoldVarb does only binary logistic regression the Multinomial menu option is an unimplemented no-operation. If you give two values of the factor group — there are only 2 here — then it does a binomial logistic regression between those two factors.
If you mention only one, it does a binomial logistic regression between that factor and all other factors in the factor group combined. Looking at the marginals is useful from the point of view of exploratory data analysis, and might suggest a recoding of variables. While categorical cases can be viewed as limit cases of a Varbul model, Varbul only analyzes data where there is variation. Once you have generated your initial cell results, discuss the effect of factors just on the percentages and report these percentages : Which class favors deletion most?
Following segment? Grammatical category? Why do you think these factors pattern the way they do? Are there any patterns that surprise you? Would you guess that all the factors in this analysis will be significantly different from one another? From the Results window, choose Binomial, 1 level.
This does a logistic regression analysis with the variables and values as defined, and produces both a Binomial Varbrul results window, and a Scattegram. In a good model, this relation should be linear. If it is badly nonlinear, this suggests interactions or other necessary factors that are not being modeled.
In the Mac version, you can click on points to identify them. This does a simple logistic regression with all the variables. Important: doing this only explores adding and deleting whole factor groups. You will also want to explore collapsing factors within factor groups. To do this, you have to use the Recode options and manually collapse together factors that you think might not have a substantially different effect. You then also have to compare log likelihoods by hand to see if the model gets significantly worse or not.
See the manual, or remember what we did in class! Report the results of the one level and stepwise analysis. Look for badly modeled cells or signs of interaction, etc. Within each factor group, are there any factors that you think should be combined? If so, combine them and present the findings of your reanalysis. The final analysis you present should be the one you think is most efficient, with the minimum number of predictive parameters required to model the data adequately.
I got a bit rushed at the end of last time. To assuage my guilt, here's a slightly more detailed discussion of comparing models to find out the best logistic regression model for the data. There are two parts to this. One is the general idea of likelihood ratio tests, and the particular instance of that for logistic regression models.
This is a useful general technique, and a good one to understand. The other half is the particularities of how this is implemented and realized in Varbrul.
Likelihood ratio tests: The likelihood ratio test here is exactly the same one we saw in week 3. It's just being used in a new context. The first fundamental idea behind the likelihood ratio test is that we would like to choose a model that gives high likelihood to the observed data. We have two different models of differing complexity, for example, one may seek to model nasal deletion based just on the type of the nasal, and the other might model nasal deletion based on the type of the nasal and the following context.
For each, we will normally have set the numeric parameters of the model to have found the maximum likelihood model within that model class. Note that if one model is a subset of the other one as in my example above , then the more complex model must score at least as well in the likelihood it assigns the data, and usually one would expect it to do at least a fraction better, since a model with more parameters can capture some of the random variation in the observed data which isn't statistically significant.
Beyond this point, we are working in the traditional hypothesis testing framework of frequentist statistics. Our null hypothesis H 0 is that the simpler model is adequate. We seek to disconfirm the null hypothesis by establishing whether there is sufficient evidence that the better fit of the more complex model cannot reasonably be attributed to modeling chance occurrences in the observed data.
The likelihood ratio is:. The likelihood-ratio chi-squared statistic G 2 will take a minimum value of 0 when the likelihood of the two models is identical, and will take high values as the more complex model becomes much more likely i. This statistic for reasonably large data sets is approximately chi-square distributed, so we test for significance against a standard chi-square distribution. Run GoldVarb. From the main screen, ask to View Tokens.
In the Tokens window that then appears, do File Load, and load the Panama data. A Groups window should appear. It should list the 4 factor groups with the factors as discussed in the preceding paragraph. Again, in Varbrul-speak, a factor group is a variable, and a factor is a categorical value of such a variable.
To make sure everything is hunky dory you might want to in the Tokens window do Action Check Tokens. This checks for things in the tokens file that are not listed in the Factor Groups specification. However, since we generated the Factors from the tokens rather than specifying them by hand, it would be rather unsettling if this check indicated any errors. GoldVarb has extensive facilities for mapping from a coding in a data file to a derived coding scheme by merging factors, or by doing more complicated things using ANDs and ORs of underlying factors.
This produces a null recoding. In any conditions file, including this null one, the first condition is treated as the dependent variable. Felicitously, this is just what we want. Click OK to anything that comes up. GoldVarb does only binary logistic regression the Multinomial menu option is an unimplemented no-operation. If you give two values of the factor group — there are only 2 here — then it does a binomial logistic regression between those two factors.
If you mention only one, it does a binomial logistic regression between that factor and all other factors in the factor group combined. Looking at the marginals is useful from the point of view of exploratory data analysis, and might suggest a recoding of variables.
While categorical cases can be viewed as limit cases of a Varbul model, Varbul only analyzes data where there is variation. Once you have generated your initial cell results, discuss the effect of factors just on the percentages and report these percentages : Which class favors deletion most?
Following segment? Grammatical category? Why do you think these factors pattern the way they do? Are there any patterns that surprise you? Would you guess that all the factors in this analysis will be significantly different from one another? From the Results window, choose Binomial, 1 level. This does a logistic regression analysis with the variables and values as defined, and produces both a Binomial Varbrul results window, and a Scattegram. In a good model, this relation should be linear.
If it is badly nonlinear, this suggests interactions or other necessary factors that are not being modeled. In the Mac version, you can click on points to identify them. This does a simple logistic regression with all the variables. Important: doing this only explores adding and deleting whole factor groups. You will also want to explore collapsing factors within factor groups. To do this, you have to use the Recode options and manually collapse together factors that you think might not have a substantially different effect.
You then also have to compare log likelihoods by hand to see if the model gets significantly worse or not. See the manual, or remember what we did in class! Report the results of the one level and stepwise analysis. Look for badly modeled cells or signs of interaction, etc.
Within each factor group, are there any factors that you think should be combined? If so, combine them and present the findings of your reanalysis. The final analysis you present should be the one you think is most efficient, with the minimum number of predictive parameters required to model the data adequately. Here's a slightly more detailed discussion of comparing models to find out the best logistic regression model for the data.
There are two parts to this. One is the general idea of likelihood ratio tests, and the particular instance of that for logistic regression models. This is a useful general technique, and a good one to understand. The other half is the particularities of how this is implemented and realized in Varbrul.
Likelihood ratio tests: The likelihood ratio test here is exactly the same one we saw in week 3.
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