Using HLM to Model Trajectories: Adolescent

Behavior as an Example from Developmental Science

Barbara J. McMorris, PhDElizabeth A. Lando-King, BSN, RN

Center for Adolescent Nursing, UMN School of Nursing

P20 Seminar ~ 22 October 2009

Objective of this P20 Seminar:

• The learner will be able to describe unique features of using an HLM approach to modeling change over time, and advantages and limitations associated with this technique.

Barbara J. McMorris, PhDSenior Associate, Center for Adolescent Nursing

Outline

• Logic of hierarchical models• Logic of growth models

– Using HLM terminology, multilevel equations– Data considerations, equations, model

building

• Applied data example– Stress Management Skills in Adolescent Girls

• Pros and Cons of HLM growth model• Relevance to Nursing

Logic of hierarchical models

• Multilevel models – what does that mean?Hierarchical Linear Modeling (HLM)

--- general set of modeling techniques

--- addresses correlated observations

“HLM” software

HLM Example: Persons within Groups

• Lucas et al. (2007)– Examined relationship between nursing home

residents’ satisfaction and nursing home characteristics

– Clustering effect within nursing homes • Problem: Single-level statistical models will not

account for clustering• Solution: Use HLM

*Significant in Combined HLM model

HLM Example: Persons within Groups (cont.)

• Factors that could affect satisfaction: – Resident level: Age, Gender*, Race, Education, Payer source,

Total ADL dependency*, cognitive function*, self-reported health*, Psychosocial distress, Daily pain*, Participation in decision making*, Length of stay

– Organizational level: • System Structure Resources: State*, Urban/rural*, Facility size,

For profit/not for profit, Multi-facility Chain/non-chain*, Acuity index• Financial Resources: %Medicaid, Occupancy rate• Clinical Resources: Special Care Unit (SCU)*, Total nurse staffing,

RN staffing, LPN staffing, CNA staffing*, Licensed Nurse (RN & LPN) Staffing

• Administrative Resources: Leadership turnover, LNHA Experience, Family council provided*

Assessing change over time: Measures within persons

First, what do we mean by time? Examples:

Seconds, hours, days, weeks, months, years Age Grade Data collection wave

Baseline, 6 mo, 12 mo, 18 mo

Consider: what is the role of time in your research question?

Time as a predictor-measure outcome at multiple occasions per person

Want to describe:1.how outcome behaves over time for

each person

2. whether other variables predict differences in change over time

Time as a Predictor of Outcomes

• Quality of life• Substance use• Antisocial behavior• Emotional intelligence

-stress management skills

-intrapersonal skills

• Treatment/medication adherence

•Relationship satisfaction•Depression•Pain management•Use of birth control•Use of condoms

Other potential predictors: gender, race/ethnicity, education, SES prior health status, treatment condition,

marital status, parenting style, etc.

Predictors may be: time-invariant or time-varying

An example of linear trajectories

Mehta and West (2000)

Logic of growth curve models

• Purpose is to model change over time

• Linear or nonlinear models possible

• Model variability in change (slopes) by modeling individual growth curves

• Variability in initial status or average change

• Predictors can be used to account for variability

time

an

tiso

cial behavio

r

time

condom

use

High variability in Intercepts and Slopes

Low variability in Intercepts and Slopes

Examples of Growth Curves

Low variability in Intercepts and High variability in Slopes

Examples of Growth Curves (cont.)

time

use

of b

irth

cont

rol

Some data considerations:

• It matters how you set up the data

• Contrast datasets– “Person-Level” approach – “Person-Period” approach

• Software programs need data to be organized in “person-period” format

Typical Data Structure: Person-Level

SUBJ STRESS_B STRESS_6 STRESS_12 STRESS_18 GROUP

01 3.43 3.60 4.60 5.37 0

02 2.18 3.87 --- 4.36 1

03 4.74 3.50 3.60 2.80 1

04 5.94 --- 4.48 5.02 1

05 4.88 4.70 5.55 5.29 1

Until N cases … … … … …

One line of data per person; multivariate format; horizontal data set; wide format

Person-Period Data

SUBJ TIME STRESS GROUP

01 0 3.40 0

01 1 3.60 0

01 2 4.60 0

01 3 5.37 0

02 0 2.18 1

02 1 3.87 1

02 2 4.36 1

03 0 4.74 1

03 1 3.50 1

03 2 3.60 1

03 3 2.80 1

Until all N people for all times

… …

Multiple lines of data per person; stacked; vertical format; long format

HLM approach to growth curves (Bryk & Raudenbush, 1992)

Level 1 describes individual change trajectories for all people in sample.

How does each person change over time?

Level 2 uses additional predictor variables to help describe change trajectories.

What predicts inter-individual differences in change?

Levels estimated simultaneously.

Level 1 (“within person”): Individual change trajectories

ijijiiij TIMEY 10

A score at a given

occasion

An initial status point

A rate of change

Some error in predicting the change trajectory

per occasion

“the change parameters”

Each person has…

Panter, 2004

Level 2 (“between person”): Predicting Level 1 trajectories

iii PREDICTOR 001000

From Level 1

iii PREDICTOR 111101

initial status

rate of change

Note: subscripts starting with 0 are about initial status;

subscripts starting with 1 are about growth rate.

Average level in the sample

Regression weights

Errors associated with these prediction models

Panter, 2004

Building an HLM growth curve model

1. Build your person-period dataset2. Look at empirical growth plots3. Fit models in a stepwise fashion:

a. Unconditional means modela. partitions variance into between and within person

b. Unconditional growth modela. Is there significant change over time?

c. Conditional modelsa. Predict initial statusb. Predict growth over time

Some design considerations

• Centering time helps... choose a meaningful “beginning of time.”

• At least three waves needed; more is better for precision

• Equal or unequal spacing of data collection waves

• Not every person needs same number data points “Missing” data are ok at level 1

• Possible to have more than 2 levels

Example: Adolescent Stress Management Skills over Time

• Research Question: Do stress management skills change over time in girls who participate in high risk sexual activities?

• Study: Prime Time (PI: Sieving)– Clinic-based youth development intervention study– Aims to reduce multiple risk behaviors

• Sample– Urban teen girls (ages 13-17) at high risk for early

pregnancy– Attending either community or school-based clinic

From Bar-On Emotioal Quotient Inventory (Youth Version)

Outcome Measure: Stress Management Scale

• When I get angry, I act without thinking.• I get upset easily.• When I am mad at someone, I stay mad for a

long time.• I get angry easily.• I have a temper.• I fight with people• I get too upset about things. • I can stay calm when I am upset.

From Bar-On Emotional Quotient Inventory (Youth Version)

Plots of all girls trajectories

Stress Management (All Participants)

1

1.5

2

2.5

3

3.5

4

Time 1 Time 2 Time 3

Time

Stre

ss M

anag

emen

t Sco

re

Plots of trajectories for “average” girl and 1 high and 1 low girl

Stress Managment (Average, High, and Low Scores)

1

1.5

2

2.5

3

3.5

4

Time 1 Time 2 Time 3

Time

Stre

ss M

anag

emen

t Sc

ores

Unconditional Growth Model Equations

• Level 1: Within-person model

Y(StressMan) = 0i (initial StressMan score)

+ 1i (Time slope) + it

• Level 2: Between-person model 0i (initial StressMan score) = γ00 (group mean) + ζ0i

1i (Time slope) = γ10 + ζ1i

*p < .01

Unconditional growth model

Parameter Estimates Coefficient Variance Reliability

Mean Stress Management

Score2.567* .354* .665

Mean Growth Rate

.087* .024* .167

Predictors of Intercept and Slope (1) Model Building

• Model 1: Adding treatment vs. control as predictor of change

Level 1: …same as before

Level 2: 0i (initial StressMan score) = γ00 (group mean) + ζ0i

1i (Time slope) = γ10 + γ11 (Treatment) + ζ1i

Predictors of Intercept and Slope(2) Model Building

• Model 2: Age predicts both intercept and

slope?

• Model 3: Clinic site predicts both

intercept and slope?

• Model 4: Use signif predictors from

Models 1-3

Predictors of Intercept and Slope (3) Results

• Model 1: Girls in treatment have

significantly steeper rate of

growth (p = 0.03)

• Model 2: Age not a significant predictor

• Model 3: Clinic site not a significant

predictor

HLM Screenshot

Estimation of parameters

• Maximum likelihood (ML): Seeks those parameter estimates that

maximize the likelihood function, which assess the joint probability of simultaneously observing all the sample data actually obtained

• Full ML: Simultaneously estimates the fixed effects and the variance components.

More complicated models

• More time points = more ways to model time change can be curvilinear, sine function, etc. See Henly’s 2008 seminar on change

functions

• Time-varying variables at Level 1 – what else besides time would be expected to

vary?

• Piecewise growth models

Pros - Advantages

• Data are modeled at individual level

• Treatment of time variable is flexible

• Model can incorporate three levels of nesting/clustering

• Non-normal data can be modeled: ordered categories, dichotomous, and

Poisson-distributed outcomes

Cons - Limitations

• Only one dependent variable at a time

• Cannot examine:– indirect effects (a.k.a. SEM models)– spurious relationships

• HLM software has its quirks– Setting up datasets from other software

packages– No missing data at level 2

Why are trajectory models important to nursing research?

• Ability to look at people within the natural context of time

• As nurses we are interested in how people function, or change, over time

• Increases real world applicability of research

• Individual focus of trajectory models

References

• Bar-On, R. (2006). The Bar-On model of emotional-social intelligence (ESI). Psicothema, 18, supl., 13-25

• Bryk, A.S. & Raudenbush, S.W. 1992. Hierarchical Linear Models: Applications and data analysis methods. Advanced quantitative techniques in the Social Sciences 1. Thousand Oaks, CA: Sage Publications.

• Lucas, J.A., Levin, C.A., Towe, T.J, Robertson, B, Akincigil, A., Sambamoorthi, U, Bilder, S, Paek, E.K., & Crystal, S. 2007. “The relationship between organizational factors and resident satisfaction with nursing home care and life.” Journal of Aging and Social Policy 19(2): 125-151.

• Mehta, P.D. & West, S.G. 2000. “Putting the individual back into individual growth curves.” Psychological Methods 5: 23-43.

• Panter, A.I. 2004 . “Analytic approaches for assessing individual and group differences in developmental change.” Methodology workshop presented to the Family Research Consortium IV, Summer Institute: Life Span Transitions, Families, and Mental Health, San Juan, Puerto Rico. Friday, July 16, 2004.

• Singer, J.D. & Willett, J.B. 2003. Applied Longitudinal Data Analysis: Modeling Change and Event Occurrence. New York: Oxford University Press, March, 2003. http://gseacademic.harvard.edu/alda/

THANK YOU!

• This presentation was supported in part by the Adolescent Health Protection Research Program (School of Nursing, University of Minnesota) grant number T01-DP000112 (PI: Bearinger) from the Centers for Disease Control and Prevention (CDC). Its contents are solely the responsibility of the authors and do not necessarily

represent the official views of the CDC.