Logistic Regression: A Self-learning Text, Third Edition (Statistics in the Health Sciences)

EXAMPLE

Model A Output: 2 2ln L¼279.317

Analysis of maximum likelihood estimates

Es

Vs

LR = –2 1n LR(A) – (–2 1n LF)

⇒

No–interaction model A

preferred to full

interaction model

= 279.317 – 275.683

= 3.634 (^) 5 df (P=0.6032)
Possibility: some product terms significant

• Carry out subchunk tests for
  EWs andEEs
  ðstart ofOption BÞ
  Reduced Model B(w/oEWterms):
  Logit PðXÞ¼aþðb 1 E 1 þb 2 E 2 Þ
  þðg 1 V 1 þg 2 V 2 Þ
  þdE 1 E 2
  Model B Output: –2ln L=277.667
  Es
  EE
  Vs
  LR = –2ln LR(B) – (–2ln LF)
  ⇒
  Reduced model B
  preferred to full
  interaction model
  = 277.667 – 275.683
  = 1.984 4 df (P=0.7387)
  EEterm:E 1 E 2 (¼PRHPAM)
  TestingH 0 :d¼0 in reduced modelB
  Wald statistic¼1.089df¼ 1 (P¼0.2122)
  LR statistic¼279.317277.667¼
  1.650df¼ 1 (P¼0.1990)
  No-interaction ModelA:
  LogitP(X)¼aþ(b 1 E 1 þb 2 E 2 )
  þ(g 1 V 1 þg 2 V 2 )
  preferred to interaction model
  The LR statistic for the overall “chunk” test
  that compares initial and reduced models
  yields a chisquare statistic of 3.634 with 5 df,
  which is highly nonsignificant. This suggests
  that theno-interaction MRSA model A is prefer-
  ableto the initial model containing five inter-
  action terms.
  Nevertheless, to consider the possibility that
  some of the product terms are significant
  despite the nonsignificant overall chunk test
  results, we now carry out a test for the
  “subchunk” ofEWs terms followed by another
  test for the “subchunk” ofEEterms (of which
  there is only one:E 1 E 2 ). We are now essentially
  considering (the start of)OptionB.
  Testing for theEW termsfirst, we present, at
  the left, the reduced model (B) obtained by
  eliminating the fourEWterms from the initial
  model, thereby keeping the singleEEterm in
  the model.
  The resulting output for this model is shown here.
  From the output, the LR statistic for the “sub-
  chunk” test that compares the initial model with
  reduced modelByields a chi-square statistic of
  1.984 with 4 df, which is highly nonsignificant.
  This suggests that thereduced model B(that
  excludes all EW terms)is preferableto the initial
  modeling containing five interaction terms.
  Focusing onthe single EE term(E 1 E 2 )inthe
  reduced modelB, we can see from the output
  for this model that the Wald test forH 0 :d*¼ 0
  is nonsignificant (P¼0.2122). The correspon-
  ding LR statistic (that compares modelAwith
  modelB) is also nonsignificant (P¼0.1990).
  The above interaction results usingOptionsA
  andBindicate that the no-interaction modelA
  shown at the left is preferable to a model
  involving anyEWorEEterms.
  Presentation: II. Modeling Strategy for Several Exposure Variables 249