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Re: st: Sparse Data Problem


From   David Airey <david.airey@vanderbilt.edu>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Sparse Data Problem
Date   Sat, 7 Mar 2009 10:40:25 -0600

.

sorry...I meant -xtmelogit- not -xtmixed- in the last email

On Mar 6, 2009, at 10:48 PM, john metcalfe wrote:

I was referring to Greenland Amer J Epi 2000.
Thanks for the tip.
John

On Fri, Mar 6, 2009 at 8:07 PM, David Airey <david.airey@vanderbilt.edu > wrote:
.

What do you mean when you said "not fully accounting for the small cell
bias"? I don't understand. I thought exact logistic models were for
situations with small cells. -nestreg- does nested estimations for logit models, though not exact logit models. It was added to Stata in June of
2008.

-Dave

On Mar 6, 2009, at 9:12 PM, john metcalfe wrote:

Dear Statalist,
I am analyzing a small data set with outcome of interest 'clstr', with the primary goal of the analysis to determine if the variables 's315t'
and 'east' have independent associations with the outcome.  However,
2315t is highly deterministic for the outcome clstr, as below. I am
concerned that exact logistic regression is not fully accounting for
the small cell bias. I would like to employ a hierarchical logistic
regression, but it seems that the stata command 'hireg' is only for
linear linear regressions??
It may be that I simply am unable to make any valid inferences with
this dataset, but I just want to make sure I have explored the
appropriate possible remedies.
Thanks,
John

John Metcalfe, M.D., M.P.H.
University of California, San Francisco


. tab s315 clstr,e

        |         clstr
  s315t |         0          1 |     Total
-----------+----------------------+----------
      0 |        22          1 |        23
      1 |        58         32 |        90
-----------+----------------------+----------
  Total |        80         33 |       113

        Fisher's exact =                 0.002
1-sided Fisher's exact =                 0.002




. logit clstr ageat s315t east emb sm num,or

Iteration 0:   log likelihood = -62.686946
Iteration 1:   log likelihood = -51.860098
Iteration 2:   log likelihood = -50.754342
Iteration 3:   log likelihood = -50.661741
Iteration 4:   log likelihood = -50.660257
Iteration 5:   log likelihood = -50.660256

Logistic regression                               Number of obs   =
100
                                               LR chi2(6)      =
24.05
                                               Prob > chi2     =
0.0005
Log likelihood = -50.660256                       Pseudo R2       =
0.1919


------------------------------------------------------------------------------
    clstr | Odds Ratio   Std. Err.      z    P>|z|     [95% Conf.
Interval]

------------- +----------------------------------------------------------------
ageatrept |   .9908837   .0139884    -0.65   0.517     .9638428
1.018683
    s315t |   9.238959   10.28939     2.00   0.046     1.041462
81.96011
east_asian |   4.219755   2.215279     2.74   0.006     1.508083
11.80727
      emb |   .9964845   .6599534    -0.01   0.996     .2721043
3.649268
       sm |   2.138175   1.696319     0.96   0.338      .451589
10.12379
num_resist |   1.064089   .2385192     0.28   0.782     .6857694
1.651116

------------------------------------------------------------------------------



Strategy 1: Two-way contingency tables

. tab clstr s315t if east==1,e

        |         s315t
  clstr |         0          1 |     Total
-----------+----------------------+----------
      0 |         6         19 |        25
      1 |         1         24 |        25
-----------+----------------------+----------
  Total |         7         43 |        50

        Fisher's exact =                 0.098
1-sided Fisher's exact =                 0.049

. tab clstr s315t if east==0,e

        |         s315t
  clstr |         0          1 |     Total
-----------+----------------------+----------
      0 |        12         33 |        45
      1 |         0          8 |         8
-----------+----------------------+----------
  Total |        12         41 |        53

        Fisher's exact =                 0.175
1-sided Fisher's exact =                 0.108



Strategy 2: Exact Logistic Regression

observation 102: enumerations =       1128
observation 103: enumerations =        574

Exact logistic regression Number of obs = 103 Model score = 19.78112 Pr >= score = 0.0000

---------------------------------------------------------------------------
clstr | Odds Ratio Suff. 2*Pr(Suff.) [95% Conf. Interval]

------------- +------------------------------------------------------------- s315t | 10.44218 32 0.0135 1.391627 474.4786 east_asian | 5.414021 25 0.0006 1.933718 16.65417




(output omitted)
observation 103: enumerations =        574

Exact logistic regression Number of obs = 103 Model score = 19.78112 Pr >= score = 0.0000

---------------------------------------------------------------------------
clstr | Coef. Score Pr>=Score [95% Conf. Interval]

------------- +------------------------------------------------------------- s315t | 2.345854 6.763266 0.0129 .3304732 6.162216 east_asian | 1.688992 12.98631 0.0004 .6594448 2.812661

---------------------------------------------------------------------------


Strategy 3: Hierarchical Regression

. hireg clstr (s315t) (east)(ageat emb sm)

Model 1:
Variables in Model:
Adding            : s315t

   Source |       SS       df       MS              Number of obs =
113
-------------+------------------------------ F( 1, 111) =
9.18
    Model |   1.7840879     1   1.7840879           Prob > F      =
0.0030
 Residual |   21.578744   111  .194403099           R-squared     =
0.0764
-------------+------------------------------ Adj R- squared =
0.0680
    Total |  23.3628319   112  .208596713           Root MSE      =
.44091


------------------------------------------------------------------------------
    clstr |      Coef.   Std. Err.      t    P>|t|     [95% Conf.
Interval]

------------- +----------------------------------------------------------------
    s315t |   .3120773   .1030162     3.03   0.003     .1079438
.5162108
    _cons |   .0434783   .0919364     0.47   0.637    -.1386999
.2256565

------------------------------------------------------------------------------

Model 2:
Variables in Model: s315t
Adding            : east

   Source |       SS       df       MS              Number of obs =
103
-------------+------------------------------ F( 2, 100) =
12.03
    Model |  4.34936038     2  2.17468019           Prob > F      =
0.0000
 Residual |  18.0778241   100  .180778241           R-squared     =
0.1939
-------------+------------------------------ Adj R- squared =
0.1778
    Total |  22.4271845   102  .219874358           Root MSE      =
.42518


------------------------------------------------------------------------------
    clstr |      Coef.   Std. Err.      t    P>|t|     [95% Conf.
Interval]

------------- +----------------------------------------------------------------
    s315t |   .2817301   .1086887     2.59   0.011     .0660947
.4973654
east_asian |   .3247109   .0843486     3.85   0.000     .1573656
.4920561
    _cons |  -.0669987   .1023736    -0.65   0.514     -.270105
.1361075

------------------------------------------------------------------------------
R-Square Diff. Model 2 - Model 1 = 0.118 F(1,100) = 14.190 p = 0.000

Model 3:
Variables in Model: s315t  east
Adding            : ageat emb sm

   Source |       SS       df       MS              Number of obs =
100
-------------+------------------------------ F( 5, 94) =
4.72
    Model |  4.36538233     5  .873076466           Prob > F      =
0.0007
 Residual |  17.3946177    94  .185049124           R-squared     =
0.2006
-------------+------------------------------ Adj R- squared =
0.1581
    Total |       21.76    99   .21979798           Root MSE      =
.43017


------------------------------------------------------------------------------
    clstr |      Coef.   Std. Err.      t    P>|t|     [95% Conf.
Interval]

------------- +----------------------------------------------------------------
    s315t |   .2335983   .1163422     2.01   0.048     .0025981
.4645984
east_asian |   .2694912   .0945411     2.85   0.005     .0817777
.4572048
ageatrept |  -.0012444   .0024199    -0.51   0.608    -.0060491
.0035603
      emb |   .0396897   .0989203     0.40   0.689    -.1567189
.2360984
       sm |   .1063985   .1087626     0.98   0.330    -.1095522
.3223492
    _cons |  -.0454117   .1512602    -0.30   0.765    -.3457423
.254919

------------------------------------------------------------------------------
R-Square Diff. Model 3 - Model 2 = 0.007 F(3,94) = 0.029 p = 0.993


Model  R2      F(df)              p         R2 change  F(df) change
p
1:  0.076   9.177(1,111)       0.003
2:  0.194  12.030(2,100)       0.000     0.118     14.190(1,100)
0.000
3:  0.201   4.718(5,94)        0.001     0.007      0.029(3,94)
0.993
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