Download - Log Linear Analysis
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HIERARCHICAL LOG-LINEAR ANALYSIS (DR SEE KI N HAI)
1. An extension of chi-square test to analyze contingency tables of 3 or more variables.
2. To determine which of the variables and their interactions best explain the observed frequencies.
3. Variables and interactions are called [Models].4. Goodness-of-fit test statistics are used to assess the degree of correspondence between the Model
and the Data.5. Statistical significance indicates the Model fails to account totally for the observed frequencies.
6. Statistical non-significance indicates the Model fits the observed frequencies7. If more than 1 Model fits the data, look for the Model that has the least variables and interactions
and the simplest one as the preferred Model.
8. Likelihood ratio chi-square is employed as the test statistics.
Assumptions
(Not as critical as parametric methods)
1. Random Sampling.
2. Similar shape and variability across the distributions.3. Independent sample.
Example.
Table below shows a 3-way contingency showing the relationship between Gender, Attitude Towards
Science and Science Achievement.
Attitude Towards Science Science Achievement Gender Margin Totals
Female Male
High High 20 30 50Low 40 25 65
Low High 35 55 90Low 45 50 95
Margin totals 140 160 300
1. Enter the data into the [Data View] and [Variable View]
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1 = High, 2 = Low
1 = Female, 2 = Male
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2. Weight cases by [Frequency]
Select [Data] then [Weight Cases..] to open the
dialogue box. Move [Frequency] into the
[Frequency Variable] box and select [Weight cases
by] then [OK].
Now the [Weight On] is shown in the [Status Bar] below
3. Select [Analyze] then [Loglinear] and [Model Selection..] to open the dialogue box. Move [Attitude],
[Achievement] and [Gender] into the [Factors] box then select [Define Range].
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4. Enter [1] into the [Minimum] box and [2] into the [Maximum] box then select [Continue].
5. Now select [Attitude] and [Define range]
Enter [1] into [Minimum] and [2] into [Maximum] and repeat for [Achievement] and select [OK].
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Interpreting the output
Extensive output is revealed by this test. It is best you ignore all and examine only the final model.
1. Ignore all the following tables:
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Likelihood ratio2
for the saturated or full model is
presented first = 0.000 and p =1.000 meaning the
saturated model provides a perfect fit for the observed
frequencies and is non-significant.
The saturated model consists of : 3 main effects
(Attitude, Achievement and Gender), 3 2-way
interactions (Attitude*Achievement, Attitude*Genderand Achievement*Gender) and 1 3-way interaction
(Attitude*Achievement*Gender)
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The saturated model includes all
components that they individually may ormay not have contributed to explaining
the variation in the observed data. Thus, itis necessary to delete components one by
one to see if this makes the models fit
worse. If it does this component of the
model iss kept for the final model. SPSS
20 begin with full model then delete each
effect in turn to determine which effects
make the least significant change in the
likelihood ratio chi-s uare.
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2. You only examine this Final Model below: The best-fitting model is presented last. In this case, the
interaction ofAchievement*Genderand the main effect ofAttitude. This model has likelihood ratio2
=3.91, DF=3 and p = 0.271 (not significant) which means the observed data can be reproduced with
these 2 effects ofAchievement*Genderand main effect ofAttitude.
To interpret the 2 effects of (a) Chi-square test of independence for Achievement and Gender,
(b) Chi-square test for Goodness of fit for Attitude (Equal expected frequencies) run the analyses
below.
How to run (a) Chi-square test of independence for Achievement and Gender
1. Select [Analyze] then [Descriptive Statistics] to select [Crosstabs..] to open the dialogue box below.
2. Move [Achievement] into [Row] and [Gender] into [Column] box, then select [Statistics] to openthe sub-dialogue box..[Crosstabs..]
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This table provides the Frequency or counts for
the data and expected frequency under this model.
Residual= Observed Count Expected Count =50.000 46.250 = 3.750.
2 statistics used for Goodness-of-fit:
1. Likelihood Ratio chi-square commonly used because it has the
advantage of being linear so that2
values can be added or
subtracted.
2. Pearson Chi-square.
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3. Select [Chi-square] and [Continue] then click on [Cells]
4. Select [Observed], [Expected] and [Unstandardized] then
[Continue] and [OK].
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How to run (b) Chi-square test for Goodness of fit for Attitude (Equal expected frequencies)
1. Select [Analyze] then [Non parametric Tests] , [Legacy Dialogs] and [Chi-Square] to open thedialogue box below.
2. Move [Attitude] into the [Test Variable List] and select [All categories equal] then click [OK]
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This table shows that
more males (85) are in
the High achievement
than the females (55)
i.e. 85/160 x 100% =53.1% for Male and
55/140 x 100%=39.3% Female
However, more
females are in the Low
achievement than the
males
We can conclude that, there was a significantassociation between the science achievement and gender
(2
= 5.75,DF=1 and p = 0.017)
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Reporting the results
A three-way frequency analysis was performed to develop a hierarchical linear model of Achievementand Attitude in Female and Male students. Backward elimination produced a model that include themain effect of Attitude and the interaction effect of Achievement and Gender. The model had a
likelihood ratio2
= 3.91, p = 0.27, indicating a good fit between the observed frequencies and the
expected frequencies generated by the model. About 38% of the students had Low Attitude score.About 53% of the male students had High Achievement score as compared with about 39% of the female
students.
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This table shows that there are morestudents in the Low Attitude score than
the High Attitude score. It is about
185/300 x 100% = 61.7% in High and38.3% in Low attitude
There was a statistical significant difference betweenthe observed and expected frequency for the 2
categories of Attitude (High and Low) towards
science (2
= 16.33,DF=1,p =0.000)
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COURSEWORK
Determine the association between the variables in the table below by using the Log-Linear Analysis.
Mental Ability Maths Achievement Gender Margin TotalsFemale Male
High High 50 30 80Low 20 15 35
Low High 35 45 80Low 20 55 75
Margin Totals 125 145 270
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