Individuals With Disabilities in Self-Employment Through Vocational Rehabilitation

Abstract

Since the passage of the Rehabilitation Act of 1973, federal and state governments have played a significant role in the employment of individuals with disabilities. In the present study, one aspect of that relationship was analyzed—individuals with disabilities who received vocational rehabilitation (VR) services to become self-employed. The authors utilized a two-level hierarchical generalized linear modeling to analyze national data from the Rehabilitation Services Administration for fiscal years 2008–2012. Among several significant (p < .001) predictors of successful VR self-employment case closure across the years, ethnicity had the largest effect, followed by gender. Although the findings from this study build on those from a previous study, conclusions about the predictors are tentative. Nevertheless, the findings add to a sparse literature on VR self-employment of individuals with disabilities, and the authors discuss the study’s implications for researchers and VR and provide suggestions for further research.

Keywords

individuals with disabilities self-employment vocational rehabilitation hierarchical generalized linear modeling

Individuals with disabilities in the United States have continued to fare poorly in employment. The U.S. Department of Labor reported that, as of February 2016, the unemployment rate of individuals with disabilities was 12.5% and 4.9% for individuals without disabilities. In addition, the labor force participation rate for individuals with disabilities was 19.5% and for individuals without disabilities was 68.2% (www.dol.gov/odep). Government has taken steps to address this problem, beginning with the Rehabilitation Act of 1973 and most recently, with passage of the Workforce Investment and Opportunities Act (2014) and subsequent amendments, whose purpose was “to empower individuals with disabilities to maximize employment, economic self-sufficiency, independence, and inclusion and integration into society … and to ensure that the Federal Government plays a leadership role in promoting the employment of individuals with disabilities” (20 U.S. Code § 9201). The Act established a mandate for state vocational rehabilitation (VR) agencies to provide employment-related services to individuals with disabilities, to help them obtain and retain employment, including self-employment. Thus, the present study focused on the role of VR in the self-employment of individuals with disabilities.

Literature Review

Since the mid-1970s, millions of individuals with disabilities in the United States have obtained employment through VR agencies. Despite that prevalence, refereed empirical research studies about employment of individuals with disabilities through the analyses of VR data over time are sparse. Such studies about self-employment are rarer. This was noted in a comprehensive review of the research literature (Yamamoto, Unruh, & Bullis, 2012), which reported that most of the refereed empirical studies were qualitative in design, in which the authors collected data through in-person interviews or surveys of VR clients and counselors but did not collect or analyze VR agencies’ data. Moreover, these studies, with small numbers of participants, focused on themes of self-employment experience of individuals with disabilities and the role of VR. One theme was the reasons individuals with disabilities gave for choosing self-employment over other options, including (a) discrimination and lack of opportunity (Blanck, Sandler, Schmeling, & Schartz, 2000; Hagner & Davies, 2002), (b) less stigmatization than other employment in the pursuit of “the American Dream”, (c) unsatisfactory previous employment experiences (McNaughton, Symons, Light, & Parsons, 2006), and (d) simply as a matter of personal choice (Callahan, Shumpert, & Mast, 2002).

The second major theme noted in the review was that the small number of studies also focused on challenges individuals with disabilities faced trying to become self-employed. Challenges included (a) lack of access to adequate financing from conventional sources, (b) perceived or actual reduction in government benefits due to their self-employment income, (c) societal prejudice, (d) negative public attitudes and low expectations, (e) educational barriers in inadequate school transition and vocational programs, (f) technological barriers in the access and use of devices, and (g) policy and regulation in business and personal supports (Callahan et al., 2002; McNaughton et al., 2006; President’s Committee on Employment of Individuals with Disabilities, 2000; Rizzo, 2002).

Recently, Yamamoto and Alverson (2013) conducted the first and only refereed empirical study of VR self-employment by analyzing federal VR data across multiple years. Utilizing multilevel analysis (i.e., hierarchical generalized linear modeling [HGLM]), they found several significant (p < .001) predictors of successful client VR case closure in self-employment, of which ethnicity and gender were reported to have had the largest effects. Further, they also found that across the United States, VR self-employment rates for fiscal years (FYs) 2003–2007 were between 2% and 2.5%, concurring with previous studies which found that since the 1990s, national VR self-employment rates have generally remained between 2% and 3% (Ipsen, Arnold, & Colling, 2005; Schriner & Neath, 1996). In context, Rissman (2003) asserted that “flows into self-employment occur during recessions and flows out of self-employment occur during economic expansions” (as cited in Hipple, 2004, p. 14).

Revell, Smith, and Inge (2009) authored, to date, the only refereed publication of empirical research comparing financial aspects of VR employment across all states and for multiple years. In 2007, the last year of their analysis, Revell et al. (2009) reported the national average weekly VR self-employment earnings at closure were US$396, whereas the national average weekly earnings for all VR employment closure outcomes were US$350. Connecticut had the highest average weekly self-employment closure earnings of US$896, compared to its average weekly earnings for all employment closures of US$538. Mississippi, the state with the highest VR self-employment closure rate had average weekly self-employment closure earnings of US$439 and average weekly earnings for all employment closures of US$423.

Blanck, Sandler, Schmeling, and Schartz (2000) completed the only empirical mixed-method research study of VR self-employment, analyzing a number of characteristics of VR clients with disabilities, service characteristics, and self-employment/entrepreneurship outcomes. Its focus was on a special statewide entrepreneurship program in Iowa for VR clients with disabilities. The study found that Caucasian males with more than a secondary education had the most successful businesses and that the overall “rate” of successful program closure far exceeded the 2–3% national VR self-employment rates.

Despite the small number of studies in the research literature, there are indications that self-employment can be a viable employment option. Over the last two decades, self-employment has become more prevalent among individuals with disabilities due in part to the (a) shift in the U.S. economy from industrial manufacturing to a high-technology, information and service-oriented economy and (b) philosophy and movement of consumer choice and self-determination in employment for individuals with disabilities (Colling & Arnold, 2007; Palmer, Schriner, Getch, & Main 2000; Rizzo, 2002; Schriner & Neath, 1996; Seekins, 1992; Walls, Dowler, Cordingly, Orslene, & Greer, 2001). Moreover, the U.S. Department of Labor (2014) reported that, among those who were employed, individuals with disabilities were more likely to be self-employed than individuals without disabilities, 11% to 6%.

As part of a larger study about self-employment of individuals with disabilities who received VR services across the United States, the present study posed three a priori research questions to gain further understanding of and to close the gaps in knowledge about VR self-employment. Moreover, by analyzing recent VR data, specifically the years during and immediately after the ‘Great Recession’, the questions also sought to uncover important patterns and changes over time.

Research Questions

In the present study, we investigated three a priori research questions:
Research Question 1: What were the significant predictors of self-employment case closure for VR clients for FYs 2008–2012?

Research Question 2: Did the significant predictors of self-employment case closure for VR clients differ across the FYs 2008–2012?

Research Question 3: Did the significant predictors of self-employment case closure for VR clients differ across the states for FYs 2008–2012?

Method

Research Design

The present study utilized a nonexperimental design with a descriptive–quantitative analysis of the extant federal data. This design was the most appropriate for the study, given its scope and purpose (see Shadish, Cook, & Campbell, 2002). The value of a descriptive study is being able to portray the characteristics of a population, group, or phenomena as it exists to generate a firm empirical basis for subsequently explaining or changing it (Tamhane & Dunlop, 2000).

The present study was a discrete and independent part of a larger mixed-method research project, which was entirely focused on self-employment of VR clients with disabilities. The present study also investigated the same three research questions as a previous study of VR self-employment (see Yamamoto & Alverson, 2013), which had analyzed extant federal data from the Rehabilitation Services Administration (RSA), the same data source, but for different years, 2003–2007.

Data Collection

The first author contacted the RSA to obtain VR data for all 50 states and Washington DC for FYs 2008–2012. These data comprised individual case-level information on all VR clients. The RSA annually collects VR data from each state, called “RSA-911,” following the end of the government’s FY.

The RSA provided data to the first author in three CD-ROMs. The data were in plain text (.txt) format and deidentified—no Social Security numbers, state ID numbers, or city/county residential information. These data were transferred to the SPSS Version 22 software for Windows (International Business Machines [IBM], 2013) to create structured SPSS data files for statistical analysis. Next, these data were aligned with their corresponding variables according to the RSA data variable dictionary (RSA, 2008). Each year’s data were inspected for missing or impossible values (i.e., keystroke error).

Defining Terms

Some of the terminology in the present study was not unique to VR or VR data, such as gender and ethnicity, but others were, such as significant disability status or the cost of VR services. In addition, VR “case” was defined by the RSA (2008) as the official record generated by a VR counselor for each prospective client. A case can be closed for any reason, but a successful closure occurs only after a client achieves an employment outcome, a job with or without supports including self-employment. Case closure with an employment outcome typically occurs when a VR counselor determines, with discretionary authority, that his or her client has demonstrated stable employment for at least 90 days. Lastly, the VR self-employment case-closure rate in the present study was defined as the number of closed cases with a self-employment outcome divided by the total number of all closed employment cases in a year.

Data Analysis

After screening the RSA data, the first author exported them to HLM 7.0 (Scientific Software International [SSI, 2014]) software for analysis. The data were considered hierarchically structured because they were “organized at more than one level” (Tabachnick & Fidell, 2007, p. 781), that is, individual VR clients “nested” within services in their home state. Hierarchically structured data need to be analyzed at different levels to avoid (a) violating the statistical assumption of independence and inflating Type I error and (b) applying group-level analysis to the individual, known as ecological fallacy (Tabachnick & Fidell, 2007, p. 782), or applying individual-level analysis to the group, known as atomistic fallacy (Hox, 2002, as cited in Tabachnick & Fidell, 2007, p. 782).

Hierarchical linear modeling, or HLM, specifically refers to the analytic technique and software by Raudenbush and Bryk (2002) in which “each of the levels in this structure is formally represented by its own submodel. These submodels express relationships among variables within a given level, and specify how variables at one level influence relations occurring at another” (p. 7). In the present study, a two-level HGLM, a nonlinear analysis of binary or multinomial outcome (criterion) variable (Raudenbush & Bryk, 2002), was produced for each FY. The level of statistical significance of the present study, given its data source and exploratory nature, was set at p < .01.

The Level-1 model of any HGLM contains three parts: (a) sampling model, (b) nonlinear link function, and (c) structural model. The sampling model is $Y_{i j} | ϕ_{i j} \sim B (m_{i j}, ϕ_{i j})$ , where Y_ij is the number of successes with a binomial distribution in m_ij number of trials and $ϕ_{i j}$ probability of success (Raudenbush, Bryk, Cheong, Congdon, & du Toit, 2011). The expected value of Y_ij is $E (Y_{i j} | ϕ_{i j}) = m_{i j} ϕ_{i j}$ and variance is $Var (Y_{i j} | ϕ_{i j}) = m_{i j} ϕ_{i j} (1 - ϕ_{i j}) .$ Also, $m_{i j} = 1$ , Y_ij may take on values of 1 or 0. This sampling model becomes a special type of binomial distribution called a Bernoulli distribution (Raudenbush & Bryk, 2002; Raudenbush et al., 2011). The sampling model for the Bernoulli distribution is rewritten as Prob $(Y_{i j} = 1 | β_{j}) = ϕ_{i j}$ . The nonlinear link function is $η = \log (\frac{ϕ_{i j}}{1 - ϕ_{i j}})$ , which is a logit or log odds link function used to transform the predicted value, η, as nonlinear (Raudenbush et al., 2011). In the present study, the link function represented the log odds of VR clients achieving self-employment closure, where ϕ _ij represents the probability of achieving self-employment closure, with values between 0 and 1, and where $1 - ϕ_{i j}$ represented the probability of achieving other employment closure. Finally, the Level-1 structural model comprised two steps. First, an unconditional model was specified in which the log odds of self-employment closure were analyzed without predictors. Second, a conditional model was specified in which the log odds of self-employment closure were analyzed with predictors. This two-step process is recommended by Raudenbush, Bryk, Cheong, Congdon, and du Toit (2011). The unconditional Level-1 structural model is written as $η = β_{0 j}$ , where β_0j is the intercept. The equation of the conditional Level-1 structural model is represented as follows:

$η_{i j} = β_{0 j} + β_{1 j} {(G e n d e r)}_{i j} + β_{2 j} {(E t h n i c)}_{i j} + β_{3 j} {(C o s t V R)}_{i j} + β_{4 j} {(E d u c A t t)}_{i j} + β_{5 j} {(P u b S u p p)}_{i j} + β_{6 j} {(S i g D i s a b)}_{i j} .$

The Level-1 structural model included an outcome variable, η _ij , representing the log odds of VR clients achieving self-employment case closure. Predictors were selected from a review of the literature. The six Level-1 predictors, X _ij were (a) gender, (b) ethnicity, (c) cost of VR services, (d) level of educational attainment at closure, (e) dollar amount of public supports (e.g., Temporary Assistance for Needy Families [TANF], Social Security Disability Insurance [SSDI]) at closure, and (f) significant disability status. The CostVR and PubSupp predictors were centered at the group (i.e., Level-2 state) mean. Centering is used when 0 is not a meaningful value in order to ensure stable estimation of model parameters (Raudenbush & Bryk, 2002). The subscript i referred to the VR client, the Level-1 unit of analysis. The subscript j referred to the state, the Level-2 unit of analysis. The six slopes, β_1j to β_6j, represented the change in the log odds of self-employment closure associated with a unit increase in the predictor, X_pij , holding constant (i.e., controlling the effects of) the other predictors.

The HGLM at Level 2 further analyzed each Level-1 coefficient β as its own outcome variable. At Level 2, the unconditional model is $β_{0 j} = γ_{00} + u_{0 j}$ . The γ₀₀ intercept represented the mean log odds of self-employment closure across states. The u _0j term represented the random effect (i.e., residual variance), which was the amount of variability among states in their mean log odds of VR self-employment case closure.

Conditional Level 2: $β_{0 j} = γ_{00} + γ_{01} (A v g U n e m p) + u_{0 j}$

$β_{1 j} = γ_{10} {Level 1 G e n d e r predictor} .$

$β_{2 j} = γ_{20} {Level 1 E t h n i c predictor} .$

$β_{3 j} = γ_{30} {Level 1 C o s t V R predictor} .$

$β_{4 j} = γ_{40} {Level 1 E d u c A t t predictor} .$

$β_{5 j} = γ_{50} {Level 1 P u b S u p p predictor} .$

$β_{6 j} = γ_{60} {Level 1 S i g D i s a b predictor} .$

In the conditional Level-2 model, the lone predictor was AvgUnemp, a state’s average annual unemployment rate. This predictor was grand mean centered. The γ₀₀ intercept term represented the mean log odds of self-employment closure for a non-White male client who had received his home state’s average cost of VR services, whose educational attainment at closure was no more than a high school level, received his state’s average dollar amount of public supports at closure, identified as not having a significant disability, and lived in a state with a “typical” self-employment closure rate, a random effect u _0j value of 0. The u _0j term represented random variation of the intercept, γ₀₀, across states, controlling for AvgUnemp. The γ₀₁ slope term represented the change in the log odds of self-employment closure associated with a unit increase in the unemployment rate for states with the same u _0j value. The remaining six terms, Level-1 slopes β_1j to β_6j, became Level-2 “outcome” variables with intercepts, γ₁₀ to γ₆₀, respectively, without the AvgUnemp predictor. These intercepts represented the mean change in the log odds of self-employment closure for VR clients in the same state who differed by one unit on the predictor, X _1j to X _6J, holding constant the other five X_ij predictors and the u _0j value. These six slope coefficients, then, were tested in the model as fixed effects at Level 2, invariant across states (see Raudenbush & Bryk, 2002; Raudenbush et al., 2011). The Level-1 and Level-2 conditional models produced the following combined complete model:

$η_{i j} = γ_{00} + γ_{01} (A v g U n e m p_{i j} - G r a n d M e a n A v g U n e m p_{i j}) + γ_{10} {(G e n d e r)}_{i j} + γ_{20} {(E t h n i c)}_{i j} + γ_{30} (C o s t V R_{i j} - G r o u p M e a n C o s t V R_{i j}) + γ_{40} {(E d u c A t t)}_{i j} + γ_{50} (P u b S u p p_{i j} - G r o u p M e a n P u b S u p p_{i j}) + γ_{60} {(S i g D i s a b)}_{i j} + u_{0 j} .$

In an HGLM, two results are produced, parameter estimates for a unit-specific model and estimates for a population-average model. Choosing one over the other is based upon the research questions specified for the analysis (Raudenbush & Bryk, 2002; Raudenbush et al., 2011). For this study, the unit-specific model was chosen because it would answer the question of how a predictor might affect state log odds or likelihood of self-employment closure, holding constant the other predictors and the Level-2 random effect value, u _0j. A population-average model would answer a different question, of how a predictor affects the nationwide (i.e., averaged across states) log odds or likelihood of self-employment closure, holding constant the other predictors but not u _0j, the random effects across states.

For the unit-specific results, model-based standard errors and robust (Huber corrected) standard errors were compared. Considerable divergence between these errors is an indication of misspecification in the distribution of u _0j random effects, which would affect inferences about the γ _xx regression coefficients (Raudenbush & Bryk, 2002). Finally, the results were examined to assess how closely the Level-1 variance followed the assumed variance of the sampling model, $m_{i j} ϕ_{i j} (1 - ϕ_{i j})$ to determine either overdispersion (i.e., more than expected) or underdispersion (i.e., less than expected) using Level-1 scalar variance, $σ^{2} w_{i j}$ (Raudenbush et al., 2011). Model parameters were estimated with restricted penalized quasi-likelihood, a type of estimation “based on normal approximation to the restricted likelihood” (Raudenbush et al., 2011, p. 112).

Results

Data Screening

Data screening revealed that approximately 3–4% of analyzed variables across the five FYs had missing data. The missing data were determined to be missing at random (see Schafer & Graham, 2002) and imputed (i.e., replaced) in SPSS Version 22 for Windows (IBM, 2013) using a recommended statistical method, multiple imputation.

A summary of the frequencies for the four RSA demographic predictors is presented in Table 1. Results indicated the largest number of employment closure cases occurred in FY 2008, with 202,297 closures, including self-employment and other employment. The smallest number of closures occurred in FY 2010, with 169,258 closures. Across the 5 years, gender of employment closures ranged from 43% to 45% female and 55% to 57% male. Ethnicity ranged from 23% to 24% non-White and 76% to 77% White. Significant disability status ranged from 6% to 7% without a significant disability and 93% to 94% with a significant disability. Educational attainment at closure ranged from 56% to 57% of clients with up to secondary level and 43% to 44% of clients with postsecondary level. Table 2 summarizes the VR case-closure status (i.e., employment and nonemployment) and the closure rates for the 5 years.

Table 1.
Client Characteristics of VR Case Closures for FY 2008–2012.

Characteristics (%) Fiscal Year

2008 2009 2010 2011 2012

Gender

Female 44.65 44.95 43.69 42.97 42.86

Male 55.35 55.05 56.31 57.03 57.14

Ethnicity

Non-White 23.49 23.84 24.19 24.27 24.28

White 76.51 76.16 75.81 75.73 75.72

Significant disability

No 7.46 6.35 6.64 6.54 7.01

Yes 92.54 93.65 93.36 93.46 92.99

Educational attainment

Postsecondary 42.54 42.72 43.63 43.84 44.19

Secondary 57.46 57.28 56.37 56.16 55.81

Note. VR = vocational rehabilitation; FY = fiscal year.

Table 2.
VR Case Closure Status and Rates for FY 2008–2012.

Case Status FY 2008 FY 2009 FY 2010 FY 2011 FY 2012

Self-employment closure 4,003 3,978 3,940 3,909 3,923

Other employment closure 198,294 174,007 165,318 171,532 173,253

No employment closure 407,328 402,310 433,556 405,817 394,799

Case closure rate 33.18 30.67 28.08 30.18 30.98

Self-employment rate 1.98 2.24 2.33 2.23 2.21

Total cases (N) 609,625 580,295 602,814 581,258 571,975

Note. VR = vocational rehabilitation; FY = fiscal year.

HGLM

The results of the HGLM analysis are presented next for the three research questions. The results are also reported by FY in Tables 3 –7.

Table 3.
Statistics for Two-Level HGLM Self-Employment Closure—FY 2008.

Fixed Effect B SE df p Exp (B) Robust SE

Unconditional model

Mean log odds intercept γ₀₀ −4.0920 .1215 50 <.001 .0167 .1203

Conditional model

Mean log odds Intercept γ₀₀ −4.5925 .1430 49 <.001 .0101 .2303

AvgUnemp γ₀₁ −.0849 .1001 49 .384 .9186 .0966

Gender γ₁₀ −.3793 .0329 202,240 <.001 .6844 .0381

Ethnic γ₂₀ .5890 .0457 202,240 <.001 1.8021 .0511

CostVR γ₃₀ .00002 .000001 202,240 <.001 1.00002 .000003

EducAtt γ₄₀ .2624 .0326 202,240 .007 1.3001 .0972

PubSupp γ₅₀ .0006 .00003 202,240 <.001 1.0006 .00007

SigDisab γ₆₀ −.0171 .0646 202,240 .895 .9830 .1301

Random effect Variance component χ² df p

Unconditional model

State mean log odds u _0j .7145 4,335.90 50 <.001

Conditional model

State mean log odds u _0j .7151 5,288.89 49 <.001

Note. HGLM = hierarchical generalized linear model; FY = fiscal year.

Table 4.
Statistics for Two--Level HGLM Self-Employment Closure—FY 2009.

Fixed Effect B SE df p Exp (B) Robust SE

Unconditional model

Mean log odds intercept γ₀₀ −3.9657 .1181 50 <.001 .0190 .1169

Conditional model

Mean log odds Intercept γ₀₀ −4.3801 .1443 49 <.001 .0125 .2350

AvgUnemp γ₀₁ −.1011 .0603 49 .065 .9038 .0536

Gender γ₁₀ −.4056 .0352 177,928 <.001 .6666 .0438

Ethnic γ₂₀ .5603 .0474 177,928 <.001 1.7513 .0641

CostVR γ₃₀ .00002 .000001 177,928 <.001 1.00002 .000002

EducAtt γ₄₀ .3319 .0347 177,928 <.001 1.3937 .0992

PubSupp γ₅₀ .0006 .00003 177,928 <.001 1.0006 .00006

SigDisab γ₆₀ −.1081 .0744 177,928 .146 .8976 .1591

Random effect Variance component χ² df p

Unconditional model

State mean log odds u _0j .6756 4,659.58 50 <.001

Conditional model

State mean log odds u _0j .6640 5,235.78 49 <.001

Note. HGLM = hierarchical generalized linear model; FY = fiscal year.

Table 5.
Statistics for Two-Level HGLM Self-Employment Closure—FY 2010.

Fixed Effect B SE df p Exp (B) Robust SE

Unconditional model

Mean log odds intercept γ₀₀ −3.9553 .1207 50 <.001 .0192 .1196

Conditional model

Mean log odds Intercept γ₀₀ −4.2499 .1382 49 <.001 .0143 .2124

AvgUnemp γ₀₁ −.0888 .0605 49 .114 .9150 .0551

Gender γ₁₀ −.3791 .0337 169,201 <.001 .6844 .0388

Ethnic γ₂₀ .5396 .0443 169,201 <.001 1.7154 .0500

CostVR γ₃₀ .00001 .000001 169,201 <.001 1.00001 .000002

EducAtt γ₄₀ .2600 .0333 169,201 .002 1.2969 .0843

PubSupp γ₅₀ .0007 .00003 169,201 <.001 1.0007 .00006

SigDisab γ₆₀ −.1973 .0559 169,201 .083 .8210 .1140

Random effect Variance component χ² df p

Unconditional model

State mean log odds u _0j .7046 5,149.21 50 <.001

Conditional model

State mean log odds u _0j .7004 6,729.58 49 <.001

Note. HGLM = hierarchical generalized linear model; FY = fiscal year.

Table 6.
Statistics for Two-Level HGLM Self-Employment Closure—FY 2011.

Fixed Effect B SE df p Exp (B) Robust SE

Unconditional model

Mean log odds intercept γ₀₀ −3.9959 .1176 50 <.001 .0184 .1164

Conditional model

Mean log odds Intercept γ₀₀ −4.2672 .1366 49 <.001 .0140 .1837

AvgUnemp γ₀₁ −.0798 .0640 49 .218 .9233 .0607

Gender γ₁₀ −.3013 .0337 175,384 <.001 .7399 .0375

Ethnic γ₂₀ .5329 .0441 175,384 <.001 1.7039 .0723

CostVR γ₃₀ .00002 .000001 175,384 <.001 1.00002 .000001

EducAtt γ₄₀ .2821 .0335 175,384 <.001 1.3259 .0745

PubSupp γ₅₀ .0007 .00003 175,384 <.001 1.0007 .00004

SigDisab γ₆₀ −.2663 .0537 175,384 <.001 .7662 .0515

Random Effect Variance Component χ² df p

Unconditional model

State mean log odds u _0j .6690 5,281.45 50 <.001

Conditional model

State mean log odds u _0j .6894 6,748.02 49 <.001

Note. HGLM = hierarchical generalized linear model; FY = fiscal year.

Table 7.
Statistics for Two-Level HGLM Self-Employment Closure—FY 2012.

Fixed Effect B SE df p Exp (B) Robust SE

Unconditional model

Mean log odds intercept γ₀₀ −4.0559 .1252 50 <.001 .0173 .1239

Conditional model

Mean log odds Intercept γ₀₀ −4.3441 .1407 49 <.001 .0130 .1802

AvgUnemp γ₀₁ −.0683 .0760 49 .373 .9340 .0851

Gender γ₁₀ −.3281 .0332 177,119 <.001 .7203 .0473

Ethnic γ₂₀ .5474 .0436 177,119 <.001 1.7286 .0703

CostVR γ₃₀ .00001 .000001 177,119 <.001 1.00001 .000002

EducAtt γ₄₀ .3268 .0329 177,119 <.001 1.3865 .0933

PubSupp γ₅₀ .0007 .00003 177,119 <.001 1.0007 .00005

SigDisab γ₆₀ −.2801 .0532 177,119 <.001 .7557 .0596

Random effect Variance component χ² df p

Unconditional model

State mean log odds $u_{0 j}$ .7559 5,183.68 50 <.001

Conditional model

State mean log odds $u_{0 j}$ .7475 6,273.83 49 <.001

Note. HGLM = hierarchical generalized linear model; FY = fiscal year.

Research Question 1: This question asked, “What were significant predictors of self-employment case closure for VR clients for FYs 2008–2012?” The significant predictors (p < .001) of self-employment case closure are presented by FY in Tables 3–7. The average unemployment of states, the lone Level-2 predictor, was not statistically significant in any year. Five Level-1 predictors were significant (p < .001) in all 5 years—gender, ethnicity, cost of VR services, educational attainment at closure (p = .007 in 2008, p = .002 in 2010), and dollar amount of public supports at closure. Significant disability status was statistically significant in 2011 and 2012.

Research Question 2: This question asked, “Did the significant predictors of self-employment case closure for VR clients differ for FYs 2008–2012?” Across the 5 years, five Level-1 significant predictors remained the same (gender, ethnicity, cost of VR services, educational attainment at closure, and dollar amount of public supports at closure). The only predictor that differed in significance was disability status, which was not statically significant in 2008–2010 but was statistically significant (p < .001) in 2011 and 2012.

Research Question 3: This question asked, “Did the significant predictors of self-employment case closure for VR clients differ across the states for FYs 2008–2012?” Across the 5 years, the significant predictors did not differ across states, however, some differences between the model standard errors and robust standard errors indicate possible significant differences in random effects among states and misspecification in random effects distribution. In FY 2008, significant predictors of closure in self-employment were the same across the states. For the educational attainment at closure predictor, however, the model-based standard error (SE = .0326) and robust standard error (SE = .0972) differed considerably, affecting the significance level, p < .001 using the model-based SE, and p = .007 using the robust SE.

In FY 2009, significant predictors of self-employment closure were the same across the states. The estimated model-based and robust standard errors differed slightly for ethnicity model based (SE = .0474) and robust (SE = .0641) and gender model based (SE = .0352) and robust (SE = .0438). The difference was largest for the educational attainment at closure predictor model based (SE = .0347) and robust (SE = .0992). These differences, however, did not result in a change to predictor significance between the two models, as both were significant at p < .001.

In FY 2010, significant predictors of self-employment closure were the same across the states. The estimated model-based and robust standard errors differed slightly for gender model based (SE = .0337) and robust (SE = .0388) and ethnicity model based (SE = .0443) and robust (SE = .0500). The standard errors differed somewhat for educational attainment at closure model based (SE = .0333) and robust (SE = .0843), changing significance level from p < .001 to p = .002. Standard errors differed most for significant disability status model based (SE = .0559) and robust (SE = .1140), changing the predictor from significant at p < .001 to not significant at p = .083.

In FY 2011, significant predictors of self-employment closure were the same across the states. The estimated model-based and robust standard errors differed slightly for gender model based (SE = .0337) and robust (SE = .0375) and significant disability status model based (SE = .0537) and robust (SE = .0515). The standard errors differed somewhat for ethnicity model based (SE = .0441) and robust (SE = .0723) and educational attainment at closure model based (SE = .0335) and robust (SE = .0745). These differences, however, did not result in a change to predictor significance between two models as both were significant at p < .001.

In FY 2012, significant predictors of self-employment closure were the same across states. The estimated model-based and robust standard errors differed slightly for significant disability status model based (SE = .0532) and robust (SE = .0596). The standard errors differed somewhat for gender model based (SE = .0332) and robust (SE = .0473), ethnicity model based (SE = .0436) and robust (SE = .0703) and educational attainment at closure model based (SE = .0329) and robust (SE = .0933). These differences did not result in a change to predictor significance in the results of the two models, as both were significant at p < .001.

Finally, the measure of overdispersion (>1.0) and underdispersion (<1.0) of Level-1 variance, as indicated by the scalar variance component ${\hat{σ}}^{2}$ , was .95 in 2008, 2010, and 2011, indicating slight underdispersion; .93 in 2012, indicating somewhat more underdispersion; and 1.05 in 2009, indicating slight overdispersion (Raudenbush et al., 2002).

Discussion

In this section, we discuss the results of the HGLM analyses for the three research questions, describe the limitations of the present study, and outline implications for stakeholders.

Research Questions

The purpose of this study was to identify predictors of VR clients’ successful self-employment case closures across recent years. To accomplish this purpose, we statistically analyzed the RSA data set using HGLM. As Gelman (2007) noted, “All models are wrong, and the purpose of model checking (as we understand it) is not to reject a model but rather to understand the ways in which it does not fit the data” (p. 349).
Research Question 1: The first research question asked, “What were the significant predictors of self-employment case closure for VR clients for FYs 2008–2012?” The conditional models in HGLM provide estimates of the log odds of self-employment closure of VR clients across states affected by six predictors at Level 1 and one predictor at Level 2 for each of the five FYs. Significant Level-1 predictors across all 5 years were (a) gender, (b) ethnicity, (c) cost of VR services, (d) educational attainment at closure, and (e) dollar amount of public supports at closure. Significant disability status was statistically significant in 2011 and 2012. In addition, the estimated log odds of self-employment, ${\hat{γ}}_{00}$ , coefficient values ranging from −4.5925 to −4.2499, were statistically significant (p < .001), indicating states (i.e., Level-2 unit) differed in their likelihood of self-employment case closure; the highest average likelihood of self-employment case closure among states occurred in 2010 (log odds coefficient of −4.2499). Looking at an individual level, each significant Level-1 predictor can increase a client’s likelihood of achieving successful self-employment case closure. For example, the probability of self-employment closure for a male, non-White VR client who received his state’s average cost of VR services, whose educational attainment at closure was no more than a high-school level, who received his state’s average dollar amount of public supports at closure, who identified as not having a significant disability, and lived in a state with a typical self-employment closure rate in FY 2008, the year with the lowest likelihood of self-employment, is 1/(1+ Exp{4.2499}) = .01406, or 1.41%. In a larger VR context, this finding also reveals that VR clients were significantly more likely to achieve closure in other employment than in self-employment.

Among the significant predictors (p < .001) across the 5 years, ethnicity was the predictor with the strongest effects (i.e., odds ratio) on self-employment closure, followed by gender and educational attainment. Ethnicity was associated with higher log odds of self-employment closure, holding constant other predictors and the random effect u _0j. The estimated regression coefficient values of ethnicity, ${\hat{γ}}_{20}$ , representing the unique effect of ethnicity fixed across states, ranged from .5329 to .5890. The largest effect was in 2008, with an odds ratio of 1.80. In other words, White VR clients had approximately an 80% increase over non-White clients in their likelihood of achieving successful self-employment closure. As previously noted, 2008 was also, on average, the year with the lowest likelihood of achieving self-employment closure at a state level. From a wider historical perspective, the disparities between White and non-White VR clients achieving successful self-employment closure is not surprising, unfortunately, as disparities between those groups have existed for decades in the U.S. economy in terms of their employment opportunities and outcomes.

Gender is associated with lower log odds of self-employment closure, holding constant other predictors and the random effect, u _0j. The estimated regression coefficient values of gender, ${\hat{γ}}_{10}$ , representing the mean fixed slopes, ranged from −.4056 to −.3013. The smallest gender effect was in 2011, with an odds ratio of .7399. That is, the odds of self-employment closure for female VR clients were .7399 times those for male clients, an odds decrease of approximately 26% for female clients. As well established historically, women and ethnic minority groups have faced substantial barriers to self-employment, in addition to those presented by disabilities (President’s Committee on Employment of People with Disabilities, 2000).

Educational attainment was associated with higher log odds of self-employment closure, holding constant other predictors and the random effect, u _0j. The estimated regression coefficient values of educational attainment, ${\hat{γ}}_{40}$ , representing the unique effect of educational attainment, with values ranging from .2600 to .3319 across the 5 years. The largest effect was in 2009, with an odds ratio of 1.39. Thus, clients with postsecondary education had approximately 39% greater likelihood than clients without postsecondary education of achieving successful self-employment closure. A strong link between VR self-employment closure and postsecondary education attainment is also documented in the empirical research literature (e.g., Blanck et al., 2000).

The two remaining significant predictors across the 5 years were (a) cost of VR services and (b) dollar amount of public supports. Although these predictors cannot be compared directly across the years because the dollar values were not adjusted for inflation (e.g., consumer price index), their effect on clients’ self-employment closure can be interpreted. Cost of VR services was associated with higher log odds of self-employment closure, holding constant other predictors and the random effect, u _0j. Estimated regression coefficients of the predictor, ${\hat{γ}}_{30}$ , represent the mean fixed slopes. The largest effect occurred in 2008, 2009, and 2011; coefficient of .00002 was the increase in the log odds of self-employment closure associated with a unit increase in the cost of VR services. The corresponding odds ratio was 1.00002. Thus, if two VR clients were similar in the other ways but differed by one unit on the cost of VR services they received, the odds of self-employment closure for the client with the higher cost of VR services were expected to be 1.00002 times the odds of the client with the lower cost of VR services, a very slight difference. In perspective, the standard deviation of this predictor in 2008 was 8,554.83. Thus, 1 standard deviation difference in the cost of VR services was associated with a change in log odds of 8,554.83 (.00002) = .1711, corresponding to an odds ratio of 1.1866, or a 19% increase in the likelihood of achieving self-employment case closure. The higher costs associated with VR self-employment cases over other employment cases have often been cited by VR counselors as a barrier to supporting clients who wish to be self-employed or who need a high level of VR support to be successful (e.g., Yamamoto et al., 2012).

Public supports were associated with higher log odds of self-employment closure, holding constant other predictors and random effect, u _0j. Estimated regression coefficients of public supports, ${\hat{γ}}_{50}$ , represent the mean fixed slopes. The largest effect was in 2010, 2011, and 2012; the coefficient of .0007 was the increase in log odds associated with a unit increase in total dollar of public supports (e.g., TANF, SSDI) received by clients. The corresponding odds ratio is 1.0007. That is, if two VR clients are similar in the other ways but differ by one unit on the dollar amount of public supports they received, the odds of self-employment closure for the client with the higher amount of public supports are expected to be 1.0007 times the odds of the client with the lower dollar amount of public supports a very slight difference.

The results of the analysis for Research Question 1 reveal that, although individual characteristics place some VR clients ahead of others in their likelihood of self-employment case closure, and that White male clients with postsecondary education are most likely to achieve VR self-employment closure, which confirms previous studies (e.g., Yamamoto & Alverson, 2013), VR clients still are significantly more likely to achieve case closure in other* employment. Case closure in self-employment continues to be extremely rare within VR, between 2% and 3% annually in the United States since the 1990s (Ipsen et al., 2005; Schriner & Neath, 1996). This is also consistent with a previous analysis of predictors of VR self-employment closure (see Yamamoto & Alverson, 2013). The very low closure rate, which has remained consistent over many years including during the recent recession and recovery, could be explained by bureaucratic inertia or other factors within the VR system, in light of the higher rates of self-employment for individuals with disabilities outside the VR system (President’s Committee on Employment of People with Disabilities, 2000).
Research Question 2: “Did the significant predictors of self-employment case closure for VR clients differ across the FYs 2008–2012?” The lone spurious statistical result occurred for the significant disability status predictor in 2010, where using the model-based standard error (SE = .0559) produced a statistically significant (p < .001) result, whereas using the robust standard error (SE = .1140) produced a nonsignificant result. The nonsignificant result is likely the correct interpretation, although, analysis of additional years of RSA data is needed for confirmation. In analyzing differences between model-based and robust standard errors, Raudenbush and Bryk (2002) noted, “Large discrepancies typically signal model misspecification” (p. 278). The fact that significant effects of the ethnicity, gender, educational attainment, cost of VR services, and public supports predictors of self-employment closure remain consistent over multiple years is noteworthy. This suggests that while an empirical trend was not established, a model trend could be examined in subsequent studies. One area of interest is to examine the contrast between the national VR self-employment rate, which reached its highest rate in 2010 (see Table 2 and Figure 1), a year after the recession ended, and the national VR employment rate for all employment closures which reached its lowest rate in 2010 (see Table 2 and Figure 2).

Research Question 3: “Did the significant predictors of self-employment case closure for VR clients differ across the states for FYs 2008–2012?” Significant predictors did not differ across states. In addition, the β_0j (log odds) state-level intercepts across the FYs, in the unconditional and conditional models, ranged from .94 to .95, indicating a high degree of reliability of intercept estimates. Reliability is based on the precision of estimation of a regression equation for each state and how much variability of the “true underlying parameters” (Raudenbush & Bryk, 2002, p. 79) occurs across states. The precision in estimating β_0j intercepts is dependent on sample size within each state (Raudenbush & Bryk, 2002). As noted previously, each RSA FY data contain around 200,000 cases of VR employment closures, thus, this criterion was very likely to have been met in the HGLM analyses. These results are not indicating, however, that state-by-state variation in the slopes was not occurring. In fact, the misspecification may be one indication of this variability, of the need to test those random effects.

Figure 1.
National VR self-employment rates for FY 2008–2012.

Figure 2.
National VR case closure rates for FY 2008–2012.

As described in the Method section, a two-step HGLM was used to analyze the RSA data, first by specifying an unconditional model (i.e., analysis without predictors), followed by a conditional model in which predictors were specified. In the unconditional models across the 5 years, the estimated log odds of self-employment closure, ${\hat{γ}}_{00}$ , were all significant (p < .001) and ranged in value from −4.0920 to −3.9553. That finding also confirmed VR clients were significantly more likely to achieve case closure for other employment than for self-employment in every state (see Table 2). In addition, the estimated variance in the states’ mean log odds of self-employment closure, ${\hat{τ}}_{00}$ , ranging from .6690 to .7559, was significant (p < .001), indicating significant differences across states in self-employment closures. The largest variance, .7559, occurred in 2012. This might be an indirect reflection of the differences among states in their rate of economic recovery from the recession. Among unconditional models, the highest odds ratio of self-employment closure was .0192, occurring in 2010. Thus, for a state with a typical self-employment closure rate, the expected odds ratio of self-employment closure was .0192, which excluded the effects of predictors. That is, for every 1 self-employment closure, approximately 50 closures would occur in other employment (1/50 = .02).

When examining differences among states’ conditional models for VR self-employment rates across the 5 years, the estimated variance of the states’ mean log odds of self-employment closure, ${\hat{τ}}_{00}$ , ranging from .6640 to .7475, were all significant (p < .001) which indicates significant differences across states in self-employment closure. That is, a VR client was more likely to achieve self-employment closure in some states than in other states. This finding parallels those of the unconditional models and is consistent with those of Yamamoto and Alverson (2013) who studied VR self-employment by analyzing RSA data for 2003–2007, and of Revell et al. (2009), who found that several states, Mississippi, Wyoming, Alaska, and Maine, had higher self-employment closure rates than other states over several years.

Limitations

No causal inferences can or should be drawn from the present study. As with any study using extant data, the data source is a limitation of the present study. The RSA requires each state to examine the data they submit for accuracy using two available editing programs (RSA, 2008), however, there is neither a mechanism for ensuring compliance nor a mechanism for ensuring all 50 states and DC conform to the same standard of data collection and reporting. These RSA data were constrained by the limited number and types of variables, and the analysis included a small number of recent years, FY 2008–2012.

Another limitation is that model misspecification in the HGLM analysis may be present as suggested by differences in the model-based and robust standard errors. Although only one predictor, significant disability status, was significantly affected, other predictors at Level 1 and Level 2 could improve model fit, while also taking due care to ensure model parsimony and avoid overfitting—predictors such as socioeconomic status or state-level economic covariates. Additional random Level-2 effects, such as those for ethnicity and educational attainment, also could be tested in subsequent analyses. In the present study, only the intercept (log odds of self-employment closure) was specified to randomly vary across states by a priori research questions.

Implications for Researchers

Understanding which variables contribute to successful VR case closure in self-employment is important for researchers, in order to understand how self-employment experience and outcomes in the VR system can differ based on the association and effects of particular individual and system factors. This study was unique in terms of its analytic approach and scope, with more than a million cases across five FYs analyzed using HGLM. Because these data are an annual “census” of VR services in the United States, they should be analyzed regularly to describe the status of self-employment and its correlates at client and state levels for multiple years to enable empirical replications and cross validations. Researchers can use these analyses to develop and test specific theories about self-employment of individuals with disabilities through VR. This study set the stage for additional analyses, as the most recent FY data from the RSA become available, to empirically confirm or refute these findings.

Although adhering to the parsimony principle, “given two different models with similar explanatory power for the same data, the simpler model is preferred” (Kline, 2005, p. 137), future research should examine additional variables that could influence self-employment closures. For example, additional variables potentially affecting self-employment closures could include client age at closure or some variable related to a client’s decision to become self-employed. Within the systems domain, the state’s cost of living, or the types of industries in the state may also affect self-employment closures. Additional support variables could include the availability of or proximity to other agencies that affect self-employment closures.

As noted previously, this study does not delve into the reasons for why self-employment case closures are not higher within the VR system. Rather, we are establishing an empirical baseline of VR self-employment closure patterns across the United States over time from which further analyses can begin to develop meaningful theoretical explanations. Given the paucity of empirical studies on the topic and the potential personal and economic impacts of employment choice and self-determination on individuals with disabilities, understanding why VR self-employment closures are very low would be informative to the field and should be the subject of future empirical studies.

Characteristics (%)	Fiscal Year
Gender
Female	44.65	44.95	43.69	42.97	42.86
Male	55.35	55.05	56.31	57.03	57.14
Ethnicity
Non-White	23.49	23.84	24.19	24.27	24.28
White	76.51	76.16	75.81	75.73	75.72
Significant disability
No	7.46	6.35	6.64	6.54	7.01
Yes	92.54	93.65	93.36	93.46	92.99
Educational attainment
Postsecondary	42.54	42.72	43.63	43.84	44.19
Secondary	57.46	57.28	56.37	56.16	55.81

Case Status	FY 2008	FY 2009	FY 2010	FY 2011	FY 2012
Self-employment closure	4,003	3,978	3,940	3,909	3,923
Other employment closure	198,294	174,007	165,318	171,532	173,253
No employment closure	407,328	402,310	433,556	405,817	394,799
Case closure rate	33.18	30.67	28.08	30.18	30.98
Self-employment rate	1.98	2.24	2.33	2.23	2.21
Total cases (N)	609,625	580,295	602,814	581,258	571,975

Fixed Effect	B	SE	df	p	Exp (B)	Robust SE
Unconditional model
Mean log odds intercept γ₀₀	−4.0920	.1215	50	<.001	.0167	.1203
Conditional model
Mean log odds Intercept γ₀₀	−4.5925	.1430	49	<.001	.0101	.2303
AvgUnemp γ₀₁	−.0849	.1001	49	.384	.9186	.0966
Gender γ₁₀	−.3793	.0329	202,240	<.001	.6844	.0381
Ethnic γ₂₀	.5890	.0457	202,240	<.001	1.8021	.0511
CostVR γ₃₀	.00002	.000001	202,240	<.001	1.00002	.000003
EducAtt γ₄₀	.2624	.0326	202,240	.007	1.3001	.0972
PubSupp γ₅₀	.0006	.00003	202,240	<.001	1.0006	.00007
SigDisab γ₆₀	−.0171	.0646	202,240	.895	.9830	.1301
Random effect	Variance component	χ²	df	p
Unconditional model
State mean log odds u _0j	.7145	4,335.90	50	<.001
Conditional model
State mean log odds u _0j	.7151	5,288.89	49	<.001

Fixed Effect	B	SE	df	p	Exp (B)	Robust SE
Unconditional model
Mean log odds intercept γ₀₀	−3.9657	.1181	50	<.001	.0190	.1169
Conditional model
Mean log odds Intercept γ₀₀	−4.3801	.1443	49	<.001	.0125	.2350
AvgUnemp γ₀₁	−.1011	.0603	49	.065	.9038	.0536
Gender γ₁₀	−.4056	.0352	177,928	<.001	.6666	.0438
Ethnic γ₂₀	.5603	.0474	177,928	<.001	1.7513	.0641
CostVR γ₃₀	.00002	.000001	177,928	<.001	1.00002	.000002
EducAtt γ₄₀	.3319	.0347	177,928	<.001	1.3937	.0992
PubSupp γ₅₀	.0006	.00003	177,928	<.001	1.0006	.00006
SigDisab γ₆₀	−.1081	.0744	177,928	.146	.8976	.1591
Random effect	Variance component	χ²	df	p
Unconditional model
State mean log odds u _0j	.6756	4,659.58	50	<.001
Conditional model
State mean log odds u _0j	.6640	5,235.78	49	<.001

Fixed Effect	B	SE	df	p	Exp (B)	Robust SE
Unconditional model
Mean log odds intercept γ₀₀	−3.9553	.1207	50	<.001	.0192	.1196
Conditional model
Mean log odds Intercept γ₀₀	−4.2499	.1382	49	<.001	.0143	.2124
AvgUnemp γ₀₁	−.0888	.0605	49	.114	.9150	.0551
Gender γ₁₀	−.3791	.0337	169,201	<.001	.6844	.0388
Ethnic γ₂₀	.5396	.0443	169,201	<.001	1.7154	.0500
CostVR γ₃₀	.00001	.000001	169,201	<.001	1.00001	.000002
EducAtt γ₄₀	.2600	.0333	169,201	.002	1.2969	.0843
PubSupp γ₅₀	.0007	.00003	169,201	<.001	1.0007	.00006
SigDisab γ₆₀	−.1973	.0559	169,201	.083	.8210	.1140
Random effect	Variance component	χ²	df	p
Unconditional model
State mean log odds u _0j	.7046	5,149.21	50	<.001
Conditional model
State mean log odds u _0j	.7004	6,729.58	49	<.001

Fixed Effect	B	SE	df	p	Exp (B)	Robust SE
Unconditional model
Mean log odds intercept γ₀₀	−3.9959	.1176	50	<.001	.0184	.1164
Conditional model
Mean log odds Intercept γ₀₀	−4.2672	.1366	49	<.001	.0140	.1837
AvgUnemp γ₀₁	−.0798	.0640	49	.218	.9233	.0607
Gender γ₁₀	−.3013	.0337	175,384	<.001	.7399	.0375
Ethnic γ₂₀	.5329	.0441	175,384	<.001	1.7039	.0723
CostVR γ₃₀	.00002	.000001	175,384	<.001	1.00002	.000001
EducAtt γ₄₀	.2821	.0335	175,384	<.001	1.3259	.0745
PubSupp γ₅₀	.0007	.00003	175,384	<.001	1.0007	.00004
SigDisab γ₆₀	−.2663	.0537	175,384	<.001	.7662	.0515
Random Effect	Variance Component	χ²	df	p
Unconditional model
State mean log odds u _0j	.6690	5,281.45	50	<.001
Conditional model
State mean log odds u _0j	.6894	6,748.02	49	<.001

Fixed Effect	B	SE	df	p	Exp (B)	Robust SE
Unconditional model
Mean log odds intercept γ₀₀	−4.0559	.1252	50	<.001	.0173	.1239
Conditional model
Mean log odds Intercept γ₀₀	−4.3441	.1407	49	<.001	.0130	.1802
AvgUnemp γ₀₁	−.0683	.0760	49	.373	.9340	.0851
Gender γ₁₀	−.3281	.0332	177,119	<.001	.7203	.0473
Ethnic γ₂₀	.5474	.0436	177,119	<.001	1.7286	.0703
CostVR γ₃₀	.00001	.000001	177,119	<.001	1.00001	.000002
EducAtt γ₄₀	.3268	.0329	177,119	<.001	1.3865	.0933
PubSupp γ₅₀	.0007	.00003	177,119	<.001	1.0007	.00005
SigDisab γ₆₀	−.2801	.0532	177,119	<.001	.7557	.0596
Random effect	Variance component	χ²	df	p
Unconditional model
State mean log odds $u_{0 j}$	.7559	5,183.68	50	<.001
Conditional model
State mean log odds $u_{0 j}$	.7475	6,273.83	49	<.001

Footnotes

Declaration of Conflicting Interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This study was supported by a research fellowship from the National Science Foundation, grant number SMA-1103370.

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Characteristics (%)	Fiscal Year
Characteristics (%)	2008	2009	2010	2011	2012
Gender
Female	44.65	44.95	43.69	42.97	42.86
Male	55.35	55.05	56.31	57.03	57.14
Ethnicity
Non-White	23.49	23.84	24.19	24.27	24.28
White	76.51	76.16	75.81	75.73	75.72
Significant disability
No	7.46	6.35	6.64	6.54	7.01
Yes	92.54	93.65	93.36	93.46	92.99
Educational attainment
Postsecondary	42.54	42.72	43.63	43.84	44.19
Secondary	57.46	57.28	56.37	56.16	55.81