Results from Exploratory Factor Analysis

May 18, 2011

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Goal

• To explore – the associations between the variables under

consideration in terms of latent “factors” around which the potential variables group

– their relative contribution to those factors– the degree to which these variables describe

a single unmeasured underlying parameter (ie. underservice)

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County-level Measures• Population to provider ratio (all provider types, age-adjusted)

• Average travel time to nearest primary care provider

• Population density

• Hispanic ethnicity

• Non-White race

• Non-White race or Hispanic ethnicity

• Limited English proficiency• Linguistically isolated• Standardized mortality ratio (SMR)• Infant mortality rate (IMR)• Low birthweight (LBW)

• Disability (age-adjusted)• Diabetes (age-adjusted)• Pap testing (age-adjusted)• Social deprivation index

(SDI)• High school drop outs• Poverty• Single mother households• Unemployed• Uninsured• Low income• Medicaid• ACSC hospitalizations• Fair/poor health• No usual provider (age-

adjusted)

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County-level measures included in final EFA

• Population to provider ratio (all provider types, age-adjusted)

• Average travel time to nearest primary care provider

• Population density

• Non-White race

• Limited English proficiency

• Standardized mortality ratio (SMR)

• Low birthweight (LBW)

• Diabetes (age-adjusted)

• Social deprivation index (SDI)

o Comprised of high school dropouts, unemployment, single mother households, and poverty

• Uninsured

• ACSC hospitalizations

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County-level measures also considered• Hispanic ethnicity

• Highly correlated with LEP, so didn’t include

• LEP vs. linguistic isolation

• Highly correlated - can’t include both. Run both ways – did not appreciably alter results; only showing results from LEP for the purposes of this presentation.

• LBW vs. IMR

• Run both ways – did not appreciably alter results; only showing results from LBW for the purposes of this presentation.

• Pap testing and disability measures from the BRFSS

• Large number of counties with missing data

• Low income and Medicaid - Highly correlated with SDI

• Components of SDI vs. the SDI itself

• Components highly correlated with other factors (ie, poverty)

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Descriptives of Variables for Counties Included in EFA (n=2856)

N Range Mean Std. Dev

LBW 2915 (3.4-15.8) 8.0 1.9

Diabetes (adj) 3141 (0.03-0.18) 0.1 0.0

SMR 3141 (0.36-2.67) 1.1 0.2

ACSC hospitalizations 3069 (24.0-319.0) 90.6 36.1

Population density 3143 (0.0-71,505.7) 260.0 1,762.3

Average travel time 3140 (0.17-174.8) 12.4 13.0

Population-to-provider ratio 3074 (105.4-202,500.0) 2,059.7 4,634.5

Non-White 3137 (0.0-0.9) 0.2 0.2

Uninsured 3140 (0.07-0.5) 0.2 0.1

LEP 3137 (0.0-0.6) 0.0 0.1

SDI 3137 (1.3-10.4) 7.3 1.9

Single mother household 3140 (2.3-44.6) 14.9 5.8

Poverty 3140 (0.0-56.7) 13.7 6.3

High school dropouts 3140 (3.0-65.3) 22.6 8.8

Unemployment 3138 (2.4-28.2) 9.0 3.2

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Three Factors Identified (n=2856 counties)

Total variance explained by three factors = 55%

Factor 1 Factor 2 Factor 3

Diabetes (age-adjusted) 0.83 0.08 -0.10

SMR 0.80 0.09 -0.06

SDI 0.75 0.17 0.28

LBW 0.72 -0.06 0.15

ACSC hospitalizations 0.56 0.24 -0.06

Population density 0.04 -0.74 0.03

Average population-weighted travel time 0.08 0.71 -0.03

Population-to-Provider ratio (all providers; age-adjusted)

0.16 0.42 -0.01

LEP -0.28 -0.22 0.74

Uninsured 0.13 0.36 0.64

Non-White race 0.42 -0.25 0.60

Variance explained post-extraction & rotation 28% 14% 13%

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Rotated Factor Loadings of County-level Measures

-1.00

-0.80

-0.60

-0.40

-0.20

0.00

0.20

0.40

0.60

0.80

0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90

Factor 1 Factor 2

Travel Time

Pop Density

P2P ratio Diabetes

SDISMR

LBWACSC

-0.20

-0.10

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

-0.40 -0.20 0.00 0.20 0.40 0.60 0.80 1.00

Factor 1 Factor 3

LEP

UninsuredNon-White

Diabetes

SDI

SMR

LBW

ACSC

-1.00

-0.80

-0.60

-0.40

-0.20

0.00

0.20

0.40

0.60

0.80

-0.20 0.00 0.20 0.40 0.60 0.80

Factor 2 Factor 3

Travel Time

Pop Density

P2P ratio

LEP

Uninsured

Non-White

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Health status/SDI Factor Independent vs. Included with other variables

Independent With other factors/

variables

Diabetes (age-adjusted) 0.81 0.83

SMR 0.82 0.80

SDI 0.77 0.75

LBW 0.67 0.72

ACSC hospitalizations 0.62 0.56

Variance explained post-extraction &/or rotation 55% 28%

In general, similar factor loadings for the health status/SDI factor whether looked at independently or with barriers and population-related variables.

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Barriers FactorIndependent vs. Included with other variables

Independent With other factors/

variables

LEP 0.71 0.74

Non-White 0.55 0.64

Uninsured 0.50 0.60

Variance explained post-extraction &/or rotation 35% 13%

In general, similar factor loadings for the barriers factor whether looked at independently or with health status, SDI and population-related variables.

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Population-related FactorIndependent vs. Included with other variables

Independent With other factors/

variables

Population density -0.74

Average travel time (population weighted) 0.71

Population-to-Provider ratio 0.42

Variance explained post-extraction &/or rotation 14%

Population-related factor is unreliable when looked at independently.

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Discussion Points/Next Steps

• How to handle population-related variables (pop-to-provider, pop density, travel time)

• Other variables to include in EFA (e.g., linguistic isolation vs. LEP)

• How to apply for weighting

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Methods• Exploratory Factor Analysis (EFA)

– The number of latent factors was unknown and had to be determined from the data

• Assumptions– Variables should be correlated, but not highly

correlated (rho>0.9)• Determinant was greater than 0 (0.012)

– Variables have a normal distribution • Natural log transformed LEP, non-White, SMR, ACSC, average

travel time, population density, and Pop-to-provider ratio

– Factor analysis is appropriate to use with these data • Kaiser-Meyer-Olkin Measure of Sampling Adequacy = 0.75

• Bartlett’s Test of Sphericity, p<0.0001

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Methods• Specifications

– Maximum likelihood method used

– Number of factors retained was based on eigenvalues (i.e., Kaiser Criterion).

• Factors with eigenvalues <1 were dropped.

• This criterion was used because we had a sample size >250 and an average communality of >0.6

– Varimax rotation to aid in interpretation• Resultant factors are not correlated with each other

• Maximizes loading of variable on one factor and minimizes its loading on all other factors (creates simple structure)

– Variables with factor loadings >0.4 (level of correlation with factor) included

• Analyses conducted in PASW Statistics v.18

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CommunalitiesProportion of variation in variable explained by the 3

factors

Extraction

Average population-weighted travel time 0.51

Population density 0.56

Diabetes 0.71

ACSC 0.38

SMR 0.65

Non-White 0.60

LBW 0.55

Population-to-Provider (all providers) 0.20

Uninsured 0.57

SDI 0.68

LEP 0.67

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Regression coefficients(for scoring purposes)

Factor

Factor 1 Factor 2 Factor 3

Avg Pop weighted travel time -0.02 0.34 0.02

Pop Density 0.06 -0.40 -0.02

Diabetes 0.31 -0.03 -0.11

ACSC 0.09 0.06 -0.03

SMR 0.25 -0.01 -0.07

Non-White 0.11 -0.15 0.28

LBW 0.18 -0.07 0.04

Population to Provider ratio 0.01 0.12 0.01

Uninsured -0.02 0.22 0.33

SDI 0.23 0.07 0.15

LEP -0.11 -0.08 0.47