# ratnose.doc
#
#   Output: ratnose.txt
#   Data:   ratnoselong.dta
#

Two drugs are being compared.  The experiment described below was to 
determine how much these drugs, which are inhaled, might irritate the 
linings of the nose, and whether the two drugs differed in this regard.

Six studies were done, each drug being studied at three concentrations (2, 
5, and 10 mg/dl).  In each study, the drug being tested was sprayed onto 
the nose tissue of twenty mice.  After a period of time, samples of the 
tissue were taken and evaluated under a microscope by a pathologist who 
scored them on the degree of changes in the cells exhibited by each sample.  
More change indicates greater irritation.  The scale used was no changes=0, 
slight changes=1, moderate changes=2, and severe changes=3.

The data, together with several Stata analyses are given in a separate 
handout [Stata appendix 1].  In discussing loglinear models, we shall use I 
for Irritation score (0, 1, 2, 3), D for Drug (1, 2), and C for 
Concentration level (1, 2, 3).

For each model description in the second column, identify which, if any, of 
the models in the first column corresponds.

 1.  (I, D, C)      ___ a. Uniform association
 2.  (ID, IC, DC)   ___ b. Saturated
 3.  (IC, D)        ___ c. Independence
 4.  (IC)           ___ d. Partial association
 5.  (IC, DC)       ___ e. Collapsed model
 6.  (ICD)          ___ f. Exactly one pair of vars conditionally dependent
 7.  None of these  ___ g. Exactly one pair of vars conditionally independent
                         
 8.  Starting with the saturated model at the top, draw a diagram which 
 shows the nesting relationships between models 1-6 above.  If model X is 
 nested within model Z, draw X at a lower level than Z and draw a line 
 connecting X to Z.

The following questions refer to the numbered Stata commands in the Stata 
appendix for this problem.

 9.  Write down the loglin command that corresponds to model [3].

10.  Compare Model [3] to Model [2].
 
     a.  Conduct the likelihood ratio test comparing these models.
         Give the value of the test statistic, its degrees of freedom, and 
         an approximate p-value.
         
     b.  What hypothesis is being tested by the test in (a)?
     
     c.  Based on (a) and (b), which model is preferable?
         
     d.  Explain in one brief sentence what (a)-(c) imply about the 
         relationships between irritation, concentration, and/or drug.
         
11.  Several variables are generated immediately before Model [4] is fit.
     What is the result of generating "conclevl", and why isn't the 
     variable "ic" defined to be irritate*conc instead of irritate*conclevl?
     
12.  Compare Model [5] to Model [4].

     a.  Conduct the likelihood ratio test comparing these models.
         Give the value of the test statistic, its degrees of freedom, and 
         an approximate p-value.
         
     b.  What hypothesis is being tested by the test in (a)?
     
     c.  Based on (a) and (b), which model is preferable?
         
     d.  Explain in one brief sentence what (a)-(c) imply about the 
         relationships between irritation, concentration, and/or drug.

13.  The FDA is interested in knowing whether one of the drugs causes 
     more irritation than the other.
     
     a.  Based on Models [1] through [5], how strong is the evidence that 
         the drugs differ?
         
     b.  Which drug causes greater irritation?
     
     c.  Describe numerically the nature of the difference in the two drugs,
         ignoring any issues of statistical significance.
         
14.  Describe how Models [8] and [9] differ from one another.

15.  Compare Model [10] to Model [9].

     a.  Conduct the likelihood ratio test comparing these models.
         Give the value of the test statistic, its degrees of freedom, and 
         an approximate p-value.
         
     b.  What hypothesis is being tested by the test in (a)?
     
     c.  Based on (a) and (b), which model is preferable?
         
     d.  Explain in one brief sentence what (a)-(c) imply about the 
         relationships between irritation, concentration, and/or drug.

16.  The FDA is interested in knowing whether one of the drugs causes 
     more irritation than the other.
     
     a.  Based on Models [6] through [11], how strong is the evidence that 
         the drugs differ?
         
     b.  Which drug causes greater irritation?
     
     c.  Describe numerically the nature of the difference in the two drugs,
         ignoring any issues of statistical significance.
         
17.  Of Models [1] through [11], which is the most useful, and why?