The Two-intercept Approach in Multilevel Modeling with SPSS

David A. Kenny

January 25, 2014

Presumed Background

• Multilevel Modeling

• Nested Design

Problem• Have multilevel data and have two

variables• How to simultaneously examine effects

for each of the two variables and allow for correlations of effects?

• How can we fool a method that estimates one equation to estimate two equations?

Examples–“Simple” bivariate analysis

– Data from two people

–Two growth curves•Two variables

•Two people

Illustrative Example• Data originally collected by Campbell, C., Lockyer, J.,

Laidlaw, T., & Macleod, H. (2007). Assessment of a matchedpair instrument to examine doctor–patient communication skills in practising doctors. Medical Education, 41, 123–129.

• A study in which each physician (level 2) has multiple patients (level 1).

• Outcome: Decision Conflict Scale or DCSUncertainty from both the patient and the doctor

(hence the two variables)Sixteen-item scale from 1 to 5

DownloadDataSyntaxOutput

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Predictors• Physician Age

•MD_Age • from 23 to 63

• Patient Age •PT_Age • from 13 to 99

• Both centered at age 40.

Sample Sizes• 162 physicians with 2 to

38 patients

• 93 physicians with 20 patients

• 2682 patients in all

Data Preparation• Stack the data• Instead of having patient and

doctor’s response on the same record for each patient, have two records one for the patient and one for the doctor.

Three New Variables– Create two dummy variables.

• Each is 0 and 1• One called MD (a 1 if from the doctor and

0 otherwise)• The other called PT (a 1 if from the

patient and 0 otherwise)– Note that MD and PT correlate -1!– Also create the variable “Role” with two

levels MD and PT (or 1 and 2).

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Downloads• Data

• Syntax

• Output

Model: Intercepts• Drop the ordinary intercept in

the model.

• Have MD and PT as predictors.

• They correspond to the individual intercepts for each of the two variables.

Fixed Effects• Predictors

–Role –Role*MD_AgeC–Role*PT_AgeC

• Note that if just MD_AgeC is put in the model, you are fixing the effect of doctor age to be the same for doctor’s the patient’s DCS.

SyntaxMIXED

dcs BY role WITH pt md pt_agec md_agec

/FIXED = role role*pt_agec role*md_agec | NOINT

/PRINT = SOLUTION TESTCOV

/RANDOM role | SUBJECT(md_id) COVTYPE(UNR)

/REPEATED = role | SUBJECT(md_id*pt_id) COVTYPE(UNR) .

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17

18

Unchecked!

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Unchecked!

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Written as One Equation

DCSMD = 1.678 + 0.002PT_AGEC - 0.007MD_AGEC + eMD

DCSPT = 1.390 - 0.007PT_AGEC + 0.002MD_AGEC + ePT

Doctors experience less decision conflict if they are older and their patients are younger.

Intercept much lower for patients than doctors.

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(1) is MD and (2) is PT (alphabetical).“Repeated Measures” are the error variances.“role[…]” are the random intercepts

Doctors with generally low

decisional conflict do not have patients

with low decisional conflict.

Variances and Correlations

Level 1 Level 2

Patent Doctor

Doctor: .131 .102

I I r .071 -.109

I IPatient: .184 .008

Some doctors generally think that there is low decisional conflict

whereas others think there is more decisional conflict.

Patients of the same doctor agree somewhat as to the doctor’s level of decisional conflict.

If a doctor thinks there was low decisional conflict with a

particular patient, that patient very

slightly agrees.

Variances and Correlations

Level 1 Level 2

Patent Doctor

Doctor: .131 .102

I I r .071 -.109

I IPatient: .184 .008Variance in how much a doctor who thinks that there is particular low or high decisional conflict with a given

patient.

Variance in how much a patient

especially experiences

decision conflict.

Alternative FormulationInstead of Doctor and Patient

Age, we could have Age of the respondent and age of the other person.

This formulation is the Actor-partner Interdependence Model or APIM.

Thank You Dr. Campbell & Dr. France Légaré!

Other Webinars

• References (pdf)

• Crossed Design

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