02 ml - testing models in spss · 5 9 step 2 null random intercept model theoretical: yij= 00 + 0j...

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MULTILEVEL MODELS

Multilevel-analysis in SPSS - step by step

Dimitri MortelmansCentre for Longitudinal and Life Course Studies (CLLS)University of Antwerp

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Overview of a strategy1. Data preparation (centering and standardizing)

2. Null random intercept model3. Random intercept with Level-1 predictors4. Adding Level-2 predictors to step 3

5. Testing random slopes level 16. Testing significant random slopes Level 17. Testing random slopes with level-2 predictors8. Reducing parameters in var-covar

9. Testing cross-level interactions10. Change estimation method and compare models11. Standardizing

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The basic formula

• General multilevel-model

Yij= 00 + 10 Xij + 01 Zj + 11 Zj Xij + u1j Xij + 0j + rij

All fixed parameters are in this part

= FIXED PART

All random parameters are in this part

= RANDOM PART

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Overview of ML models

Model

0RI Null random intercept / Intercept only / Unconditional means

RI Random intercept

FR Fully Random

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PHASE 1: PREPARATION1. Data preparation

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STEP 1 Data preparation

Actions:

• Look at the distribution of variables• Check outliers

• Data centering and standardizing• Check your centering and standardizing

(see slides data management)

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PHASE 2: VARIANCE COMPONENT MODELS2. Null random intercept model3. Random intercept with Level-1 predictors4. Adding Level-2 predictors to step 3

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PHASE 2

2. Null random intercept model• PURPOSE: estimate a basic model to compare

other models with

3. Random intercept with level-1 variables• PURPOSE: how much variance can be explained

with your level-1 predictors ?

4. Random intercept with level 1 and level 2 variables• PURPOSE: how much (additional) variance can

be explained with your level-2 predictors ?

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STEP 2 Null random intercept model

THEORETICAL: Yij= 00 + 0j + rij

In the example:00 = Overall intercept: mean income over all countries

0j = Non explained differences in income between the countries

rij = Non explained differences in income between the individuals

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* 2. STEP 2: Null random intercept model;* **********************************************;

MIXED ink_centr/PRINT = SOLUTION TESTCOV/METHOD = REML/FIXED = INTERCEPT/RANDOM = INTERCEPT | SUBJECT(cntry2).

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* 2. STEP 2: Null random intercept model;* **********************************************;


Put the Dependent variable after MIXED

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* * 2. STEP 2: Null random intercept model;* **********************************************;


PRINTSOLUTION = Show the Fixed effects in the output

with the standard errorsTESTCOV = Show significance tests for the

variance components

METHOD The estimation methodUsed method here = Restricted Maximum Likelihood

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* * 2. STEP 2: Null random intercept model;* **********************************************;


FIXEDAdd the fixed variables (independent variables) here.

RANDOMAdd the random parts here. HERE we add only the intercept (for now).

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OUTPUT FOR: Yij= 00 + 0j + rij

Grouping variable

Number of parameters in the model

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OUTPUT FOR: Yij= 00 + 0j + rij with

Estimated mean incomeover all countries is -0.097

200j :0,N ~ 2

ij 0,N ~ rr

Unexplained variance (differences) on Country level (level 2) equals 2.4855

Unexplained variance (differences) on individuea level equals 4.0058

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• Summary table

0RI

Intercept -0.097596

σ²r 4.005854

σ²0 2.485587

σ²1 //

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• No explanation of the variance in income• BUT a decomposition of the variance in income

in 2 parts

σ²0 = Inter-group variance: differences between countries

σ²r = Intra-group variance: differences between individuals

QUESTION: Are there enough differences between countries to justify a multi-level analysis ?

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QUESTION: Are there enough differences between countries to justify a multi-level analysis ?

ANSWER: Intra-class correlation-coefficient (RHO)

1 = σ²0 / (σ²0 + σ²r)

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Intra-class correlation-coefficient (RHO) (1 = σ²0 / (σ²0 + σ²r) )

1 = 2.4842 / (2.4842 + 4.0076) = 0.383

INTERPRETATION: 38.3 % of the total variance can be ascribed to level 2.

PUT DIFFERENTLY: For 38.3 %, the differences in income between countries in the ESS are due to differences between countries (richer and poorer countries). 61.7 % is due to differences in individuals within these countries (richer and poorer individuals within a country).

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STEP 3 Random intercept (level 1)

THEORETICAL: Yij= 00 + 10 Xij + 0j + rij




10 Xij = General slope of the independent variable X (gender or education)

QUESTION: How much of the original variance in 0j has been explained now ?

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BASIC IDEA:Add all your level-1 predictors

De variance components in the residuals should become smaller BECAUSE the level-1 predictors now take up a part of the explanation of the total variance.

QUESTION: How big is the explained part ?

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* 3. STEP 3: Random intercept model with level 1 predictors;* **********************************************************************;

MIXED ink_centr BY geslacht WITH opl_centr/PRINT = SOLUTION TESTCOV/METHOD = REML/FIXED = INTERCEPT geslacht opl_centr/RANDOM = INTERCEPT | SUBJECT(cntry2).

WITH: treat the independent as a continuous variableBY: treat the independent as a categorical variable

Add your Level-1 independent variables

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OUTPUT FOR: Yij= 00 + 10 Xij + 0j + rij

Error-variance on level 2

Overall intercept


200j :0,N ~ 2

ij 0,N ~ rr

Coefficients at level-1

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OUTPUT FOR: Yij= 00 + 10 Xij + 0j + rij 200j :0,N ~ 2

ij 0,N ~ rr

The effect of gender and education on income is significant.

Even after controlling for level-1 predictorsthere still are significant differences between individuals on level-1 and significant differences between the countries on level 2.

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Reduction of individual differences:

From 4.0058 to 3.4640

Reduction of differences between countries:

From 2.4855 to 2.1303

Is this enough ? We need an R²-measure

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Regression-like R²-measure on level 1:

rBasis - rModel / rBasis 4.0058 - 3.4640 / 4.0058

Regression-like R²-measure on level 2:

Basis - Model / Basis 2.4855 - 2.1303 / 2.4855

BUT: The estimation methods make this easy solution erroneous.

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No consensus yet about a good R²-measure.

Correction of Bosker&Snijders (1994) – level 1:

(rBasis + Basis) - (r Model + Model) / (rBasis + Basis)


(rBasis + (Basis /n) )-(r Model + ( Model/n) ) / (rBasis + (Basis/n) )

Whereby n = mean cluster size at level 2

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STEP 3 Random intercept (level 1)Correction of Bosker&Snijders (1994) – level 1:

(rBasis + Basis) - (r Model + Model) / (rBasis + Basis) = 0.14


(rBasis + (Basis /n) )-(r Model + ( Model/n) ) / (rBasis + (Basis/n) ) = 0.14

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STEP 4 Random intercept (level 1+2)

THEORETICAL : Yij= 00 + 10 Xij + 01 Zj + 0j + rij





01 Zj = Direct effect of country variables on income (BNP or religion)

QUESTION: How much variance in 0j from step 3 is now further explained ?

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BASIC IDEA:Look how much the level 2 predictors can

explain (as a group)

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* 4. STEP 4: Random intercept model with level 1 and level 2 predictors;* *********************************************************;

MIXED ink_centr BY geslacht WITH opl_centr bnp_centr bnppps_centr romkath_centr relig_centr /PRINT = SOLUTION TESTCOV/METHOD = REML/FIXED = INTERCEPT geslacht opl_centr bnp_centr bnppps_centr romkath_centr relig_centr /RANDOM = INTERCEPT | SUBJECT(cntry2).

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OUTPUT FOR: Yij= 00 + 10 Xij + 01 Zj + 0j + rij 200j :0,N ~ 2

ij 0,N ~ rr


Overall intercept


Coefficients on level-1


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ij 0,N ~ rr

BNPPPS and % Roman Catholics are significant, BNP and Religiosity not.

Even after controlling for level-2 predictorsthere still are significant differences between individuals on level-1 and significant differences between the countries on level 2.

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ij 0,N ~ rr

Problem with BNP ?

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Reduction of individual differences:

3 vs 2 From 3.464 to 3.4763 vs 1 From 4.006 to 3.476

Reduction of country differences:

3 vs 2 From 2.130 to 0.5523 vs 1 From 2.486 to 0.552

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Pseudo – R² = 0.38


Pseudo – R² = 0.78

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Preliminary conclusions:

1. The error-variance on level 2 is only significant to the 0.006 level.

2. Two level-2 variables do not seem to work in this model: BNP and Religiosity. We remove them from the model when they are less important from a theoretical perspective.

3. Our model strongly explains differences on level 2. But also on the individual level the explanatory power of the independent variables is satisfactory.

PHASE 3: testing random slopes5. Testing random slopes level 16. Testing significant random slopes Level 17. Testing random slopes with level-2 predictors8. Reducing the parameters in var-covar

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PHASE 35. Testing random slopes level 1

• PURPOSE: looking which level-1 predictor has significant slopes (without the level-2 predictors).

6. Testing significant random slopes Level 1• PURPOSE: joining all significant random slopes from

step 5 in one model

7. Testing random slopes with level-2 predictors• PURPOSE: adding the level 2 predictors back to

model, including the random slopes from step 6

8. Reducing parameters in var-covar• PURPOSE: simplifying the model (removing non-

significant co-variances) in order to ease the estimation of the model.

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STEP 5 Testing random slopes level 1

THEORETICAL : Yij= 00 + 10 Xij + 1j Xij + 0j + rij





1j Xij = Differences in slopes (effect) of variable X (gender or education) between the countries

REMARK: No longer country differences in this model !REMARK : Model is estimated for each independent variable on level 1 separatelyQUESTION: Are there significant differences in the effect of X between the countries?

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BASIC IDEA:Until now we did not allow for differences in

slopes of the independent variables at level 1.

FOR EACH INDEPENDENT, we will test if there are significant differences in slopes at level-2.

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* STEP 5: Testing the significance of the random slopes step-by-step.***********************************************************************************;

MIXED ink_centr BY geslacht WITH opl_centr/PRINT = SOLUTION TESTCOV/METHOD = REML/FIXED = INTERCEPT geslacht opl_centr/RANDOM = INTERCEPT opl_centr | SUBJECT(cntry2) COVTYPE(UN).

COVTYPE should be “Unstructured”.

We make eduction RANDOM here.

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OUTPUT FOR: Yij= 00 + 10 Xij + 1j Xij + 0j + rij




Overall intercept

2ij 0,N ~ rr

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1j

0j:0,N ~

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Structure of the variance-covariance matrix

Theoretical:

In SPSS:

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1j

0j :0,N ~

2,21,2

1,1

UNUN

UN

01991.003258.0

1123.2

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In SPSS:

2,21,2

1,1

UNUN

UN

01991.003258.0

1123.2

The random slope is significant on the 0.01 level.MEANING: there is a significant different effect of education between the countries

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* STEP 5: Testing the significance of the random slopes step-by-step.**********************************************************************************.

MIXED ink_centr BY geslacht WITH opl_centr/PRINT = SOLUTION TESTCOV/METHOD = REML/FIXED = INTERCEPT geslacht opl_centr/RANDOM = INTERCEPT geslacht | SUBJECT(cntry2) COVTYPE(UN).

Gender is made RANDOM here.

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Overall intercept

2ij 0,N ~ rr

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1j

0j:0,N ~

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Theoretical:

In SPSS:

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1j

0j :0,N ~

2,21,2

1,1

UNUN

UN

6207.04728.0

144.1

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Evaluation of the random slope of gender

In SPSS:

2,21,2

1,1

UNUN

UN

The random slope of the dichotomous variable gender can not be tested. If you include “gender” as a continuous variable in the model, this random slope turns out to be significant.

0097.004622.0

1725.2

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Conclusion:

- Education and gender have significant slopes between the countries.

- Gender is only estimable when you include the variable as a continuous measure.

BUT: the effect of gender is unclear.

In this example I will keep gender in the model with a random slope (only for educational purposes).

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STEP 6 Testing random slopes level 1+2

THEORETICAL : Yij= 00 + 10 Xij + 1j Xij + 0j + rij

00 = Overall intercept: mean income over all countries





Theoretically this is the same model as in step 5 but now we include ALL significant random slopes in the model.

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* STEP 6: Including all level-1 variables with significant random slopes.* ****************************************************************************************.

MIXED ink_centr BY geslacht WITH opl_centr/PRINT = SOLUTION TESTCOV/METHOD = REML/FIXED = INTERCEPT geslacht opl_centr/RANDOM = INTERCEPT opl_centr geslacht | SUBJECT(cntry2) COVTYPE(UN).

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2ij 0,N ~ rr

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1j

0j:0,N ~

Equal digits are error-variances:

UN(1,1) Intercept

UN(2,2) Error-variance of education

UN (3,3) Error-variance of gender

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OUTPUT FOR: Yij= 00 + 10 Xij + 1j Xij + 0j + rij 2ij 0,N ~ rr

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1j

0j:0,N ~

Equal digits are error-variances:

UN(1,1) Intercept

UN(2,2) Error-variance of education Significant on the 0.01 level

UN (3,3) Error-variance of gender NOT significant: SO: Gender NOT random in the model!

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STEP 7 Testing random slopes with level-2 predictors

THEORETICAL : Yij= 00 + 10 Xij + 01 Zj + 1j Xij + 0j + rij







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BASIC IDEA:We now check which influence the level-2

predictors have on income in a model with random slopes (= step 6).

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* STEP 7: Including all level-2 variables in the model of step 6*. ******************************************************************************.

MIXED ink_centr BY geslacht WITH opl_centr bnppps_centr romkath_centr/PRINT = SOLUTION TESTCOV/METHOD = REML/FIXED = INTERCEPT geslacht opl_centr bnppps_centr romkath_centr /RANDOM = INTERCEPT opl_centr | SUBJECT(cntry2) COVTYPE(UN).

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OUTPUT FOR: Yij= 00 + 10 Xij + 01 Zj + 1j Xij + 0j + rij




Overall intercept

2ij 0,N ~ rr

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1j

0j:0,N ~


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OUTPUT FOR: Yij= 00 + 10 Xij + 01 Zj + 1j Xij + 0j + rij 2ij 0,N ~ rr

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1j

0j:0,N ~

Significant differences remain on level 2 for the effect of education

Both the predictors on level 1 as on level 2 are significant.

Significant differences remain between the intercepts of the countries.

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STEP 8 Simplifying the model

THEORETICAL : Yij= 00 + 10 Xij + 01 Zj + 1j Xij + 0j + rij







We now look at the variance-covariance matrix

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Differences in intercept and slope between units of level 2.

Yij= 00 + 10 Xij + 1j Xij + 0j + rij

These are the conditions:

rij ~ N(0, σ²r)

This is the covariance between the random intercepts and the random slopes for variabele Xij.

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1j

0j :0,N ~

If this covariance is significant (= different from 0), then it means that the changes in intercepts is systematicallycorrelated to the changes in slopes.

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Model intercept Slopes Covariance

FR many many Negative

FR many many Positive

FR many manyNot

significant (0)

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With 1 independent X-variable on level 1

With 2 independent X-variables on level 1

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1j

0j :0,N ~

Covariance between the random intercepts and the random slopes for variabele Xij.

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2j

1j

0j

:0,N ~

2 independents = 3 covariances

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With 3 independent X-variable on level 1

With random slopes models, the number of parameters to be estimated increases very rapidly.

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3j

2j

1j

0j

:0,N ~

3 independents = 6 covariances

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3j

2j

1j

0j

:0,N ~

Non-significant covariances = The covariances is not significantly different from 0.

SO: We might as well fix these to 0.

CONSEQUENCE: Each fixed covariance is one parameter less to be estimated.

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3j

2j

1j

0j

:0,N ~

SPSS does not allow to fix each separate covariance to 0.

BUT: there is an option to fix all co-variances to 0 in one time.

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3j

2j

1j

0j

:0,N ~

COVTYPE(UN)

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3j

2j

1j

0j

000

00

0:0,N ~

Without COVTYPE

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Look at the (significance of) the co-variances in the output of step 7

Covariance is NOT significant

Consequence: Estimate the model in STEP 7 again without the COVTYPE-option.

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•STEP 8: Reduction of parameters in var-covar matrix•*********************************************************.

MIXED ink_centr BY geslacht WITH opl_centr bnppps_centr romkath_centr/PRINT = SOLUTION TESTCOV/METHOD = REML/FIXED = INTERCEPT geslacht opl_centr bnppps_centr romkath_centr /RANDOM = INTERCEPT opl_centr | SUBJECT(cntry2).

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The co-variances are fixed at 0 : there is no estimation of co-variances any more. Only the variances are given in the output.

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PHASE 4: Refining and finishing9. Testing cross-level interactions10.Change the estimation method and compare your

models11.Standardizing

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PHASE 4

9. Testing cross-level interactions• PURPOSE: checking if level-2 predictors correlate

with level-1 predictors

10.Changing the estimation method and comparing models• PURPOSE: Compare models with Full Maximum

Likelihood

11.Standardizing• PURPOSE: Estimating the end model again with

standardized variables to check the relative influence

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STEP 9 Testing cross-level interactions

THEORETICAL : Yij= 00 + 10 Xij + 01 Zj + 01 Zj Xij + 1j Xij + 0j + rij







01 Zj Xij = Interaction of country variables and individual variables on income

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What is an interaction effect ?

A (significant) interaction effect shows how the effect of one independent variable changes within the levels of another independent variable.

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• In regular OLS regression

EG. Interaction between gender and education:

How does the effect of education on income change between boys and girls?

• In multilevel regression

EG. Interaction between education and GDP:

How does the effect of education on income change for countries with a different GDP ?

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TWO BASIC PRINCIPLES

1.When an interaction effect is significant, the main effects NEED TO BE included in the model.

EG: When the interaction effect between education and GDP_PPS is included THEN you also need the main effect of education and the main effect of GDP_PPS in the model.

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2. When an interaction effect is present in a model, the main effects have a different meaning.

Meaning without interaction-effect- Education: the change in income when the educational

level rises with one unit

- BNP_PPS: the change in income when BNP_PPS rises with one unit

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2. When an interaction effect is present in a model, the main effects have a different meaning.

Meaning without interaction-effect- Education: the change in income when the educational

level rises with one unit at a level of 0 from BNP_PPS

- BNP_PPS: the change in income when BNP_PPS rises with one unit at a level of 0 from education

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* * STEP 9: Testing cross-level interactions* **********************************************************************.

MIXED ink_centr BY geslacht WITH opl_centr bnppps_centr romkath_centr/PRINT = SOLUTION TESTCOV/METHOD = REML/FIXED = INTERCEPT geslacht opl_centr bnppps_centr romkath_centr

opl_centr*bnppps_centr/RANDOM = INTERCEPT opl_centr | SUBJECT(cntry2).

Specifying an interaction effect = repeating both variables with * between both.

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Main effects (both are significant)

Interaction effect (not significant)

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How to interpret the interaction effect ?(if it had been significant)

1. Interpret the main effects

2. Choose an interpretation perspective

3. Write the regression equation for one of the independent variables

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Interpretation 1. Interpret the main effects

Main effect education: When BNPPPS_centr is equal to 0, someone's income will increase with 0.5192 scale points when his educational level increases with one unit.

Main effect GDP: When education is equal to 0, someone's income will increase with 0.0265 scale points when his countries BNP_PPS increases with one unit.

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Interpretation 1. Interpret the main effects

Because of the centering (mean = 0) we can also say:

Main effect education: At a mean BNPPPS_centr level, someone's income will increase with 0.5192 scale points when his educational level increases with one unit.

Main effect GDP: At a mean educational level, someone's income will increase with 0.0265 scale points when his countries BNP_PPS increases with one unit.

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Interpretation 2. Choose an interpretation perspective

2 perspectives:

1. How does the effect of education on income changes for different levels of BNP_PPS ?

2. How does the effect of BNP_PPS on income changes for different levels of education ?

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Interpretation 2. Choose an interpretation perspective

“How does the effect of education on income changes for different levels of BNP_PPS ?”

is theoretically the only possibility here.

BECAUSE: BNP_PPS will not change if people have a higher degree. But the educational effects can indeed change for countries with different BNP_PPS.

BUT REMEMBER: Statistically, both perspectives are always possible.

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Interpretation 3. Work out the regression equation

PERSPECTIVE: How does the effect of education on income changes for different levels of BNP_PPS ?

- Write out the regression equation for education, when BNP_PPS takes on different levels.

- WHICH levels of BNP_PPS ? Usually: minimum, 25th percentile, median, mean, 75th

percentile and maximum.

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STEP 1: Search in the EXAMINE output for the values of the minimum, 25th percentile, median, mean, 75th percentile and the maximum of BNPPPS_centr.

EXAMINE VARIABLES=bnppps_centr/PERCENTILES(25,75) /STATISTICS DESCRIPTIVES.

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STEP 1: Search in the EXAMINE output for the values of the minimum, 25th percentile, median, mean, 75th percentile and the maximum of BNPPPS_centr.

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STEP 1

Minimum -65.8815Q1 -23.2815Mean 0Median 2.1185Q3 14.6185maximum 126.9125

Remark: We assume that the other independent variable also take on the value of 0 (and disappear from the equation).

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Minimum Income = -0.2532 + 0.5192 opleiding + 0.0265 (-65.88) + 0.0008 OPL*(-65.88)Q1 Income = -0.2532 + 0.5192 opleiding + 0.0265 (-23.2815) + 0.0008 OPL*(-23.2815)Median Income = -0.2532 + 0.5192 opleiding + 0.0265 (0) + 0.0008 OPL*(0)Mean Income = -0.2532 + 0.5192 opleiding + 0.0265 (2.1185) + 0.0008 OPL*(2.1185)Q3 Income = -0.2532 + 0.5192 opleiding + 0.0265 (14.6185) + 0.0008 OPL*(14.6185)maximum Income = -0.2532 + 0.5192 opleiding + 0.0265 (126.92) + 0.0008 OPL*(126.92)

Income = -0.2532 + 0.5192 education + 0.0265 BNPPPS + 0.0008 EDUC*BNPPPS

STEP 2: Vul in

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Minimum Income = -1,999 + 0,4665 OPLQ1 Income = -0,8702 + 0,5006 OPLMedian Income = -0,1971 + 0,5209 OPLMean Income = -0,2532 + 0,5192 OPLQ3 Income = 0,1342 + 0,5309 OPLmaximum Income = 3,11 + 0,6207 OPL

Income = -0.2532 + 0.5192 education+ 0.0265 BNPPPS + 0.0008 EDUC*BNPPPS

STEP 2: Vul in

Cfr main effect of education when BNP_PPS is equal to 0 (see the main effect in the output).

Interpretation interaction effectThe effect of education rises (very slightly) as BNP_PPS increases.

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STEP 10 Comparing models with Full Maximum Likelihood

• Estimation in multilevel analysis

- Maximum Likelihood

- Generalized Least Squares (not in SPSS)- Generalized Estimation Equations (not in SPSS)- Markov Chain Monte Carlo (not in SPSS)- Bootstrapping (not in SPSS)

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• Maximum Likelihood

- Maximizing the likelihood function- Population parameters are estimated in such a way

that the probability of finding that particular model is maximized with the data at hand.

- TWO versions: Full Maximum Likelihood (ML)Restricted Maximum Likelihood (REML)

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• Restricted Maximum Likelihood

- Only the variance components are used in the estimation.

- Standard in SAS (but not in SPSS) and in almost all multilevel programs

- Best estimation for the variance components

- CONSEQUENCE: Gives you the best estimation for the parameters and you should use this estimation method to obtain your parameters

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• Full Maximum Likelihood

- Variance components and regression coefficients are involved in the estimation.

- Disadvantage: Variance components are underestimated.

USEFULL ?- Easier estimation method- The difference between two models can be used in a

chi²-difference test (is not possible with REML !).

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• CONSEQUENCE

- Use REML for all models

- Use ML at the end to compare estimated models with each other.

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* STEP 10: Using Full Maximum Likelihood to compare models.* ************************************************************************************.

*Step2.

MIXED ink_centr/PRINT = SOLUTION TESTCOV/METHOD = ML/FIXED = INTERCEPT/RANDOM = INTERCEPT | SUBJECT(cntry2).

Use Method=ML (or leave the METHOD line out).

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Use the difference in DEVIANCE (-2 LOG LIKELIHOOD) and the difference in degrees of freedom in a Chi²-difference test

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• Calculating the degrees of freedom of your model

Calculating the degrees of freedom by hand:

Intercept 1

Error variance level-1 1

Fixed slopes on level-1 p

Error-variances for slopes on level-1 p

Co-variances of slopes and intercept p

Co-variances between the slopes p(p-1)/2

Fixed slopes on level-2 q

Slopes for cross-level interactions p*q

Whereby:

p = number of level-1 predictorsq = number of level-2 predictors

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Make an overview table with tests

DEVIANCE D(f)Prob. Chi² vs null

modelProb. Chi² vsprevious model

STEP 2 Null random intercept model 141642,268 2

STEP 3 Random intercept with level-1 136763,937 9 0,000

STEP 4 Random intercept w level 1 and 2 122423,421 13 0,000 0,000

STEP 6 Random slopes model 136407,950 9 0,000

STEP 7 Random slopes with level-2 122075,321 11 0,000 0,000

STEP 8Random slopes with level-2

(reduction)122077,357 7 0,000 0,729

STEP 9 Cross level interactions 122077,357 12 0,000 1,000

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STEP 7 Random slopes with level-2 122075,321 11 0,000 0,000

STEP 8Random slopes with level-2

(reduction)122077,357 7 0,000 0,729

STEP 9 Cross level interactions 122077,357 12 0,000 1,000

This is the basic model.

In the fourth column, you compare with this model

Chi²-difference test

- Test value = 141642.268 – 136763.937 = 4878- Degrees of freedom = 9 – 2 = 7

- Result: Probability = 0.000

- Interpretation: The model in STEP3 is a significant improvement of the Null random intercept model (STEP 2)

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STEP 7 Random slopes met level-2 122075,321 11 0,000 0,000

STEP 8Random slopes met level-2

(reductie)122077,357 7 0,000 0,729

STEP 9 Cross level interacties 122077,357 12 0,000 1,000

Comparison with the Null random intercept model (STEP 2)

Interpretation: Is this model a significant improvement vs STEP 2 ?

Comparison with the previous model (= STEP 3)

Interpretation: Is this model a significant improvement vs STEP 3?

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STEP 3 Random intercept met level-1 136763,937 9 0,000

STEP 4 Random intercept met level 1 en 2 122423,421 13 0,000 0,000


STEP 7 Random slopes met level-2 122075,321 11 0,000 0,000

STEP 8Random slopes met level-2

(reductie)122077,357 7 0,000 0,729

STEP 9 Cross level interacties 122077,357 12 0,000 1,000

BE CAREFULL here !!

Previous model is the model with co-variances. SO is the model without co-variances a significant worsening vs. the previous model ?

CONSEQUENCE: A probability higher than 0.05 points to a good model.

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STEP 11 The final model with standardized variables

• Standard output of multilevel models = not standardized.

• Interpretation in original (scale) units

• DISADVANTAGE: no comparison of the actual size of the parameters.

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• 2 methods

1. Estimate the last model again with standardized variables

(disadvantage = variance components also change)

2. Standardize the parameter by hand

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METHOD 1

* STEP 11: Standardising in order to compare parameters. * ********************************************************************************************;

MIXED ink_std BY gesl_std WITH opl_std bnppps_std romkath_std/PRINT = SOLUTION TESTCOV/METHOD = ML/FIXED = INTERCEPT geslacht opl_std bnppps_std romkath_std/RANDOM = INTERCEPT opl_std | SUBJECT(cntry2).

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METHOD 2

Stand. Coeff. = (non stand. Coeff) x (stan dev INdep.)(stan dev DEpendent)

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METHOD 2

DESCRIPTIVES VARIABLES=ink_centr geslacht opl_centr bnppps_centr romkath_centr /STATISTICS=STDDEV.

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RESULT:

Nonstandardized Standardized Non

standardized Standardized

Gender 0,281 0,06 BNP PPS 0,027 0,40

Education 0,519 0,31 % Rom Cath -0,095 -0,15

MULTILEVEL MODELS

Multilevel-analysis in SPSS - step by step

Dimitri MortelmansCentre for Longitudinal and Life Course Studies (CLLS)University of Antwerp

02 ml - testing models in spss · 5 9 step 2 null random intercept model theoretical: yij= 00 + 0j...

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