JPP Online Supplemental Materials for Multivariate Multilevel Survival

Models (MMSA)

Mike Stoolmiller: stoolmil@uoregon.eduUniversity of Oregon

8/14/13

Instructions To Readers

• Important information is presented in both the slides and in the notes window.

• Important information is also in the manuscript and this powerpoint will be best understood when used in conjunction with the manuscript.

Outline

• Example Research Question & Application• MMSA Path Diagram for Example Application• Coding Dyadic (parent-child) Microsocial

Interaction• Restructuring Microsocial Data for Analysis• Mplus Syntax for Example Application

Example Application• Research Question: When confronted by a negative parent

as in a discipline encounter are antisocial children quicker to use anger and slower to use sad/fear emotions relative to normal children?

• Analytic Strategy: Use MMSA to look at child transitions from dyadic state of parent negative-child neutral.

• Child can transition from neutral to either positive, anger or sad/fear. By hypothesis, anger transitions will be elevated, sad/fear transitions depressed and positive transitions unaffected for antisocial relative to normal children.

• Parent can transition from negative to either positive or neutral but parent transitions ignored for simplicity.

Path Diagram For A Multivariate Multilevel Dyadic States Model

Within Dyad Level

Between Dyad Level

X2, 3rd Grade Child Antisocial

X1, Kinder Child

Antisocial

DurationNcRpPcRp

Censored? (yes=1,no=0)

fAcRp NcRpAcRp

DurationNcRpAcRp

Censored?(yes=1,no=0)

DurationNcRpScRp Censored?

(yes=1,no=0)

fPcRp NcRpPcRp

fScRp NcRpScRp

Residual NcRpAcRp

Log h0,AcRp(t) NcRpAcRp

Base Hazard

Coding Dyadic Interaction• Two separate streams of event durations in proper

temporal order, one for each dyad member but synchronized to a common time line as shown in the schematic event history diagram.

• Coding system has exhaustive and mutually exclusive categories so the behavior of each dyad member is known at all times.

• Two streams can be merged to form a single stream for the dyad that categorizes the behavior of the dyad at all times.

• Coding system does not introduce artificial dependencies between the streams (e.g., single stream coding with precedence rules).

Schematic Event History Diagram

Parent

1st

NcNp

0 5 10 15 20 25 30 35 40 45 50 55

ChildEpisode Time

P

N

R

P

N

A

S

2nd

NcRp

Session Time

0 8 0 6 0 3 0 3 0 6 0 8 0 5 0 5 0 13

3rd

AcRp

4th

AcNp

5th

NcNp

6th

NcRp

7th

ScRp

8th

ScNp

9th

NcNp

Dyad

Restructuring Dyadic Data• Starting from two separate streams in two separate files for

one individual dyad: • First, merge the two streams using time as the merge key using

standard database merging routines to get a dyadic stream.• Second, fill in missing values arising from merge and compute

dyadic state indicator.• Third, use lead or lag functions to compute start and end state

and start and end time for each dyadic state. Compute duration for each dyadic state, end time minus start time.

• Fourth, add a dyad ID variable, repeat for all individual dyadic files and concatenate (stack) in to one large file for entire sample.

• More operations are necessary on the stacked file but are explained later. Example data comes from event history schematic diagram.

Time Child0 N

14 A20 N34 S44 N57 E

Time Parent0 N6 R

17 N26 R39 N57 E

Merge on Time

Time Child Parent0 N N6 R

14 A17 N20 N26 R34 S39 N44 N57 E E

Step 1: Merge On Time

Time Child Parent Dyad0 N N NcNp6 N R NcRp

14 A R AcNp17 A N AcNp20 N N NcNp26 N R NcRp34 S R ScRp39 S N ScNp44 N N NcNp57 E E EcEp

Time Child Parent0 N N6 R

14 A17 N20 N26 R34 S39 N44 N57 E E

Back Fill

Step 2: Back Fill Missing Values And Create Dyadic State Indicator

Time Child Parent Dyad0 N N NcNp6 N R NcRp

14 A R AcNp17 A N AcNp20 N N NcNp26 N R NcRp34 S R ScRp39 S N ScNp44 N N NcNp57 E E EcEp

Start State

End State

Start Time

End Time

Duration

NcNp NcRp 0 6 6NcRp AcNp 6 14 8AcNp AcNp 14 17 3AcNp NcNp 17 20 3NcNp NcRp 20 26 6NcRp ScRp 26 34 8ScRp ScNp 34 39 5ScNp NcNp 39 44 5NcNp EcEp 44 57 13

Step 3: Use Lead & Lag And Compute Duration

Lead & Lag

Start State

End State

Start Time

End Time Duration

Dyad ID

NcNp NcRp 0 6 6 123NcRp AcNp 6 14 8 123AcNp AcNp 14 17 3 123AcNp NcNp 17 20 3 123NcNp NcRp 20 26 6 123NcRp ScRp 26 34 8 123ScRp ScNp 34 39 5 123ScNp NcNp 39 44 5 123NcNp EcEp 44 57 13 123

Repeat & Stack

Step 4: Add Dyad ID, Repeat For All Dyads And Stack

Time Child0 N

14 A20 N34 S44 N57 E

Time Parent0 N6 R

17 N26 R39 N57 E

Time Child Parent Dyad0 N N NcNp6 N R NcRp

14 A R AcNp17 A N AcNp20 N N NcNp26 N R NcRp34 S R ScRp39 S N ScNp44 N N NcNp57 E E EcEp

Merge on Time

Start State

End State

Start Time

End Time Duration

NcNp NcRp 0 6 6NcRp AcNp 6 14 8AcNp AcNp 14 17 3AcNp NcNp 17 20 3NcNp NcRp 20 26 6NcRp ScRp 26 34 8ScRp ScNp 34 39 5ScNp NcNp 39 44 5NcNp EcEp 44 57 13

Lead & Lag

Time Child Parent0 N N6 R

14 A17 N20 N26 R34 S39 N44 N57 E E

Fill

Repeat & Stack

Censoring

• A waiting time is censored if we stop observing and do not know how much longer it took for the event to finally happen.

• In microsocial interaction, waiting times will be censored by the end of the observation period, equipment malfunction, if the subject moves out of sight of observer, etc.

• In addition, waiting times for competing transitions are also censored by the transition that actually happened, so called “competing risks”.

Competing Risks and Censoring

• In the example model, the start state is always the same but there are 3 possible child transitions to 3 different end states.

• An actual child transition that happens will censor the waiting times for the other 2 child transitions.

• It is not known how long it would take for either of the other 2 transitions to happen, just longer than the transition that did happen.

• This is known as “competing risks” and is illustrated in the schematic diagram.

Schematic of Censoring In Competing Risks

Time0 1 32

Parent Negative-Child Neutral

Parent Negative-Child

Anger

Parent Negative-

Child Positive

ObservedNot Observed:

Censored

Parent Negative- Child Sad

Censoring Indicators• Mplus requires a dichotomous censoring indicator that is scored

0 if a particular transition actually happened and 1 if censored for any reason.

• Each of the 3 types of child transitions in the model needs a corresponding censoring indicator.

• These censoring indicators can be easily computed in the stacked file by using a series of conditional compute statements.

• For example if AcRp is the name of the censoring indicator:– If (endstate equal to “AcRp”) then AcRp = 0;– If (endstate not equal to “AcRp”) then AcRp = 1;

• This needs to be done outside of Mplus because Mplus does not read or use character data.

Censor IndicatorsStart State

End State Duration AcRp PcRp ScRp

Dyad ID

NcNp NcRp 6 1 1 1 123NcRp AcRp 8 0 1 1 123AcRp AcNp 3 1 1 1 123AcNp NcNp 3 1 1 1 123NcNp NcRp 6 1 1 1 123NcRp ScRp 8 1 1 0 123ScRp ScNp 5 1 1 1 123ScNp NcNp 5 1 1 1 123NcNp EcEp 13 1 1 1 123

Data Structure Including Censoring Indicators

Duration Variables

• In parallel to the censoring indicators, Mplus requires a separate duration variable for each type of transition in the model.

• The example model has 3 types of child transitions so 3 duration variables, one for each type of transition are required.

• In the data as currently structured, there is only 1 duration so 2 more copies of the existing duration variable need to be computed and named appropriately.

• This can be easily done in Mplus and it works well to name each duration to match its corresponding censoring indicator.

Duration Variables Censor IndicatorsStart State

End State AcRp_ Dur PcRp_Dur ScRp_Dur AcRp PcRp ScRp

Dyad ID

NcNp NcRp 6 6 6 1 1 1 123

NcRp AcRp 8 8 8 0 1 1 123

AcRp AcNp 3 3 3 1 1 1 123

AcNp NcNp 3 3 3 1 1 1 123

NcNp NcRp 6 6 6 1 1 1 123

NcRp ScRp 8 8 8 1 1 0 123

ScRp ScNp 5 5 5 1 1 1 123

ScNp NcNp 5 5 5 1 1 1 123

NcNp EcEp 13 13 13 1 1 1 123

Data Structure Including Duration Variables

Suggested Spss Syntax

• Syntax for steps 1-4 for example data shown in notes window.

Mplus Syntax For Cox MMSA Model

• In addition to the standard syntax required for a 2-level model in Mplus:

• VARIABLES: – SURVIVAL = AcRp_dur (ALL) PcRp_dur (ALL)

ScAp_dur (ALL);– TIMECENSOR = AcRp PcRp ScRp;

• ANALYSIS: basehazard = off;• Full syntax in notes window.

The End