Loglinear contingency table analysis
Download
1 / 28

Loglinear Contingency Table Analysis - PowerPoint PPT Presentation


  • 243 Views
  • Updated On :

Loglinear Contingency Table Analysis. Karl L. Wuensch Dept of Psychology East Carolina University. The Data. Weight Cases by Freq. Crosstabs. Cell Statistics. LR Chi-Square. Model Selection Loglinear. HILOGLINEAR happy(1 2) marital(1 3) /CRITERIA ITERATION(20) DELTA(0)

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about 'Loglinear Contingency Table Analysis' - niveditha


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
Loglinear contingency table analysis

Loglinear Contingency Table Analysis

Karl L. Wuensch

Dept of Psychology

East Carolina University







Model selection loglinear
Model Selection Loglinear

HILOGLINEAR happy(1 2) marital(1 3)

/CRITERIA ITERATION(20) DELTA(0)

/PRINT=FREQ ASSOCIATION ESTIM

/DESIGN.

  • No cells with count = 0, so no need to add .5 to each cell.

  • Saturated model = happy, marital, Happy x Marital



The model fits the data perfectly chi square 0
The Model Fits the Data Perfectly, Chi-Square = 0

  • The smaller the Chi-Square, the better the fit between model and data.


Both one and two way effects are significant
Both One- and Two-Way Effects Are Significant

  • The LR Chi-Square for Happy x Marital has the same value we got with Crosstabs


The model parameter mu
The Model: Parameter Mu

  • LN(cell freq)ij =  + i + j + ij

  • We are predicting natural logs of the cell counts.

  •  is the natural log of the geometric mean of the expected cell frequencies.

  • For our data,

    and LN(154.3429) = 5.0392


The model lambda parameters
The Model: Lambda Parameters

  • LN(cell freq)ij =  + i + j + ij

  • i is the parameter associated with being at level i of the row variable.

  • There will be (r-1) such parameters for r rows,

  • And (c-1) lambda parameters, j, for c columns,

  • And (r-1)(c-1) lambda parameters, for the interaction, ij.



Main effect of marital status
Main Effect of Marital Status

  • For Marital = 1 (married),  = +.397

  • for Marital = 2 (single),  = ‑.415

  • For each effect, the lambda coefficients must sum to zero, so

  • For Marital = 3 (split), = 0 ‑ (.397 ‑ .415) = .018.


Main effect of happy
Main Effect of Happy

  • For Happy = 1 (yes),  = +.885

  • Accordingly, for Happy =2 (no),  is ‑.885.


Happy x marital
Happy x Marital

  • For cell 1,1 (Happy, Married),  = +.346

  • So for [Unhappy, Married],  = -.346

  • For cell 1,2 (Happy, Single),  = -.111

  • So for [Unhappy, Single],  = +.111

  • For cell 1,3 (Happy, Split),  = 0 ‑ (.346 ‑ .111) = ‑.235

  • And for [Unhappy, Split], = 0 ‑ (‑.235) = +.235.


Interpreting the interaction parameters
Interpreting the Interaction Parameters

  • For (Happy, Married),  = +.346 There are more scores in that cell than would be expected from the marginal counts.

  • For (Happy, Split),  = 0 ‑.235

    There are fewer scores in that cell than would be expected from the marginal counts.


Predicting cell counts
Predicting Cell Counts

  • Married, Happy e(5.0392 + .397 +.885 +.346) = 786 (within rounding error of the actual frequency, 787)

  • Split, Unhappy

    e(5.0392 + .018 -.885 +.235) =82, the actual frequency.


Testing the parameters
Testing the Parameters

  • The null is that lambda is zero.

  • Divide by standard error to get a z score.

  • Every one of our effects has at least one significant parameter.

  • We really should not drop any of the effects from the model, but, for pedagogical purposes, ………


Drop happy x marital from the model
Drop Happy x Marital From the Model

HILOGLINEAR happy(1 2) marital(1 3)

/CRITERIA ITERATION(20) DELTA(0)

/PRINT=FREQ RESID ASSOCIATION ESTIM

/DESIGN happy marital.

  • Notice that the design statement does not include the interaction term.


Uh oh big residuals
Uh-Oh, Big Residuals

  • A main effects only model does a poor job of predicting the cell counts.


Big chi square poor fit
Big Chi-Square = Poor Fit

  • Notice that the amount by which the Chi-Square increased = the value of Chi-Square we got earlier for the interaction term.


Pairwise comparisons
Pairwise Comparisons

  • Break down the 3 x 2 table into three 2 x 2 tables.

  • Married folks report being happy significantly more often than do single persons or divorced persons.

  • The difference between single and divorced persons falls short of statistical significance.


Spss loglinear
SPSS Loglinear

LOGLINEAR Happy(1,2) Marital(1,3) /

CRITERIA=Delta(0) /

PRINT=DEFAULT ESTIM /

DESIGN=Happy Marital Happy by Marital.

  • Replicates the analysis we just did using Hiloglinear.

  • More later on the differences between Loglinear and Hiloglinear.


Sas catmod
SAS Catmod

options pageno=min nodateformdlim='-';

data happy;

input Happy Marital count;

cards;

1 1 787

1 2 221

1 3 301

2 1 67

2 2 47

2 3 82

proccatmod;

weight count;

model Happy*Marital = _response_;

Loglin Happy|Marital;

run;


Pasw genlog
PASW GENLOG

GENLOG happy marital

/MODEL=POISSON

/PRINT=FREQ DESIGN ESTIM CORR COV

/PLOT=NONE

/CRITERIA=CIN(95) ITERATE(20) CONVERGE(0.001) DELTA(0)

/DESIGN.


Genlog coding
GENLOG Coding

  • Uses dummy coding, not effects coding.

    • Dummy = One level versus reference level

    • Effects = One level versus versus grand mean

  • I don’t like it.


Catmod output
Catmod Output

  • Parameter estimates same as those with Hilog and loglinear.

  • For the tests of these paramaters, SAS’ Chi-Square = the square of the z from PASW.

  • I don’t know how the entries in the ML ANOVA table were computed.