Predictors of Life Satisfaction in Frail Elderly doc

Predictors of Life Satisfaction
in Frail Elderly
Soleman H. Abu-Bader, PhD
Anissa Rogers, PhD
Amanda S. Barusch, PhD
ABSTRACT. This study examined the relationship between life satisfac
-
tion and physical status, emotional health, social support and locus of
control in the frail elderly. A random sample of 99 low-income, frail el-
derly living in the community was interviewed. Almost 40% of partici-
pants reported high levels of life satisfaction. Multiple regression analysis
identified four significant predictors of life satisfaction: Perceived physical
health, social support, emotional balance, and locus of control. Physical
health emerged as the most significant predictor of life satisfaction ac-
counting for 14% of the variance. Social support, emotional balance and lo-
cus of control each accounted for an additional 6% of the variance in life
satisfaction. All four predictors explained 32% (R = .57) of the total vari-
ance in life satisfaction. Implications for practice and recommendations are
discussed.
[Article copies available for a fee from The Haworth Document Deliv
-
ery Service: 1-800-HAWORTH. E-mail address: <>
Website: <> © 2002 by The Haworth Press, Inc. All rights
reserved.]
Soleman H. Abu-Bader is Assistant Professor, School of Social Work, Howard Uni
-
versity.
Anissa Rogers is Assistant Professor, Department of Social and Behavioral Sciences,
University of Portland.
Amanda Barusch is Professor, Graduate School of Social Work, University of Utah.
Address correspondence to: Soleman H. Abu-Bader, PhD, Howard University, 601

Howard Place, NW, Washington, DC 20059 (E-mail: ).
This study was funded by the Goodwill Family Foundation.
Paper presented at the 4th Annual Conference of the Society for Social Work & Re
-
search, Charleston, South Carolina, January 29-31, 2000.
Journal of Gerontological Social Work, Vol. 38(3) 2002
/>Ó 2002 by The Haworth Press, Inc. All rights reserved. 3
KEYWORDS. Frail, elderly, life satisfaction, physical health, social sup
-
port, cognitive status, emotional balance, locus of control, life events, ac
-
tivities of daily livings
The life satisfaction of the elderly has been widely researched and dis
-
cussed. The construct is particularly important for professionals, such as
social workers, whose work aims to enhance the quality of life of the el
-
derly. Much research in this area has analyzed how life satisfaction is in
-
fluenced by factors such as social support, financial status, physical
health, and locus of control. Most of this work has been conducted with
healthy, community-dwelling elders. No studies to date have considered
the life satisfaction of elders who have significant physical limitations
(possibly because of a tendency to assume that physical problems will re
-
sult in low life satisfaction). The purpose of the current study is to expand
on prior studies by analyzing factors that may influence life satisfaction
among frail elders.
FACTORS INFLUENCING LIFE SATISFACTION
AMONG THE ELDERLY

Factors that influence life satisfaction include environmental character-
istics, such as the availability of social support, and personal traits, such as
self-esteem, physical health, financial resources, a sense of
connectedness, and locus of control.
Social Support and Life Satisfaction
Several studies have examined the relationship between social sup
-
port and life satisfaction among the elderly. Most of this literature has
indicated a positive relationship between social support and life satis
-
faction. One study conducted by Aquino, Russell, Cutrona, and
Altmaier (1996), found that social support was significantly related to life
satisfaction. Aquino et al. surveyed 301 community-dwelling elders aged
65 years old and over to determine how demographic variables such as fi
-
nancial status, educational level, and work patterns affect life satisfaction.
Results from face-to-face interviews indicated that elders who were work
-
ing or volunteering showed higher life satisfaction than those who were
not working or volunteering. Further, these authors found that participants
who engaged in volunteer work had more social supports than those who
4 JOURNAL OF GERONTOLOGICAL SOCIAL WORK
were not engaged in volunteer work, which in turn led to higher levels of
life satisfaction. The findings also indicated that participants who reported
low education and socioeconomic levels and who had poor physical
health indicated that they had few social supports and low life satisfaction.
Consequently, participants who were not functioning well enough to work
or volunteer had fewer opportunities to build social networks, which af
-
forded fewer opportunities to engage in satisfying relationships outside of

the workplace than participants who were working or volunteering.
Though many of the measures used in the aforementioned study were
standardized, particularly those measuring social support and life satisfac
-
tion, it is unclear whether these instruments are appropriate for use with
older adults.
In another study conducted by Newsome and Schulz (1996), 5,201
people aged 65+ were randomly selected from Medicare lists. Partici
-
pants were surveyed to gather information regarding their social net-
works, level of functioning, perceived social supports, and life
satisfaction. Results indicated that participants who reported decreased
physical functioning also perceived their social supports as poor. Further,
participants who perceived their social supports as poor reported low life
satisfaction. Thus, participants who reported physical difficulties also per-
ceived their social supports to be poor, which may have affected their
level of life satisfaction.
At this point the theoretical connection between physical functioning
and social support remains unclear. While some argue that social support
enhances physical health or buffers an individual from the deleterious ef-
fects of stress, these connections have not been empirically demonstrated.
Personal Traits
Other studies have indicated that factors such as self-esteem, per
-
ceived physical health, and locus of control are associated with life sat
-
isfaction (Girzadas, Counte, Glandon, & Tancredi, 1993; Rogers,
1999). Still other literature posits that financial security and a sense of
closeness and connectedness with others predict life satisfaction
(Fisher, 1995; Girzadas et al., 1993; Gray, Ventis, & Hayslip, 1992;

Kahana et al., 1995; Levitt, Antonucci, Clark, Rotton, & Finley, 1986;
McGhee, 1984; Revicki & Mitchell, 1986; Wing-Leung Lai & McDon
-
ald, 1995). Indeed, Kahana et al. (1995) found that short-term problems
such as those caused by financial difficulties and changes in relationships
through retirement or death may have a significant impact on life satisfac
-
tion.
Abu-Bader, Rogers, and Barusch 5
Locus of control has been another widely studied construct in relation
to life satisfaction among the elderly. Most research has focused on the
relationship between internal, external, and chance locus of control and
life satisfaction, and conclusions as to the nature of this relationship
have been mixed. In an exploratory study conducted by Girzadas et al.
(1993), 258 community-dwelling individuals aged 55+ were selected
from a larger study that examined the relationship between health status,
locus of control, and life satisfaction. The larger study recruited partici
-
pants from the rolls of Health Maintenance Organizations and private
physicians. Results from face-to-face interviews with participants indi
-
cated that functional health status was positively associated with life satis
-
faction. Further, participants who scored high on chance locus of control
also scored low on life satisfaction. Specifically, participants who re
-
ported poor physical health and who demonstrated a tendency toward be
-
lieving their health outcomes were based on chance also showed relatively
low life satisfaction.

Results from other studies suggest that individuals with a tendency to-
ward internal locus of control, particularly with regard to physical health,
show higher levels of life satisfaction than those who show a tendency to-
ward external or chance locus of control (e.g., Haber, 1994; Searle, M. S.,
Mahon, M. J., & Iso-Ahola, S. E., 1995; Wing-Leung Lai & McDonald,
1995). It follows that older adults who are not internally focused may
show a tendency toward low life satisfaction. For instance, Park and
Vanderberg (1994) found from a sample of 154 individuals aged 58+ that
those who demonstrated low levels of personal autonomy and high levels
of dependency tended to be more negatively affected by poor health and
showed a need for social support in the form of a confidant than more au
-
tonomous and independent individuals. Moreover, Vallerand, O’Connor,
and Blais (1989) found that older adults living in nursing homes that did
not allow for personal autonomy or self-determination showed lower life
satisfaction than older adults living in nursing homes that allowed for
more personal independence or those living independently in the commu
-
nity.
Conversely, some studies have indicated that older adults who demon
-
strate a tendency towards external locus of control have higher life satis
-
faction than those with an internal or chance locus of control (e.g., Haber,
1994; Rogers, 1999). It may be that older individuals who are externally
focused and who have developed trust in their health care provider actu
-
ally demonstrate higher levels of life satisfaction than those who rely on
themselves or even chance for health care decisions. Specifically, the lat
-

ter group may experience more guilt or feelings of hopelessness when
6 JOURNAL OF GERONTOLOGICAL SOCIAL WORK
faced with health problems, poor treatment, or poor decision making with
regard to health care (Haber, 1994).
In summary, studies of life satisfaction among elderly have identified
several important constructs that may influence this measure. These con
-
structs include the following: social support, physical health, locus of con
-
trol (internal, external, and chance), financial status, and life events. Using
multiple regression analysis, the current study incorporated these and
other measures to develop a model that best describes factors associated
with life satisfaction among frail elderly.
METHODOLOGY
Sample
Recruiting Methods. Participants for this study were randomly selected
from clients of The Alternatives Program (TAP) in Salt Lake County,
Utah. TAP provides services such as adult day care and homemakers to
low-income adults whose physicians certify that they are at risk of nursing
home placement. Of the 182 TAP clients contacted, 102 (56%) were inter-
viewed, of whom 99 were 60 years old and over and thus included in the
final analysis. Of the 99 subjects, 87 (88%) were women. Program staff
provided access to demographic information on non-participants, and
independent t-tests and chi-square analyses were conducted to identify
differences in age, race, gender, income, and living status (whether or
not the respondent lived alone) between participants and non-partici-
pants. These analyses yielded significant differences in age (t = 2.42, p =
.017). Older TAP clients refused to participate in the study more fre
-
quently. Analyses revealed no significant differences on other variables.

The most common reason for non-participation, given by 43% of those
who declined, related to poor health and cognitive difficulties. Others
(26%) indicated they just did not want to be interviewed, while the re
-
mainder cited other reasons.
Participant Characteristics. Participants in this study were predomi
-
nantly white (94%). Their mean age was 78 years (SD = 8.5) with a range
from 60 to 101 years. The median monthly income was $575 with a range
from $257 to $1,584 per month. The vast majority (81%) were either wid
-
owed (53%) or divorced (28%). The majority (70%) lived alone. The
modal level of education was high school (34%).
Respondents were frail, needing assistance with an average of 2.6 Ac
-
tivities of Daily Living (ADL’s) and 5.3 Instrumental Activities of Daily
Abu-Bader, Rogers, and Barusch 7
Living (IADL’s). Respondents reported their health to be “fair” (38%) to
“good” (24%).
Over one third (36%) had a diagnosis relating to the musculoskeletal
system, primarily a form of arthritis. The next most common diagnostic
category was neurological, with 24% of the sample experiencing an ill
-
ness of this kind. This was followed by cardiovascular illness, experi
-
enced by 19% of the sample. The mean duration of illness was 14 years,
with a range from 1 to 70. Half (53%) of the sample reported a steady de
-
cline associated with their illness. Others reported that their conditions
were stable (16%) or had variable “up and down” trajectories (14%). A

few respondents (10%) reported their condition had recently improved.
Data Collection
Interviews. Trained undergraduate and graduate MSW students con-
ducted in-depth interviews in respondents’ homes. Interviews lasted one
to three hours. When participants became fatigued, interviewers com-
pleted the interview in a second home visit. While most of the protocol
was highly structured, interviews closed with a “guided conversation” de-
signed to explore respondents’ understanding of the impact of physical ill-
ness on their lives and emotional well-being. For individuals with
significant cognitive impairment, interviews were conducted with visual
aids and additional time was allowed.
Instruments. A general demographic section recorded age, gender,
race, religion, education, marital status, participant’s occupation,
spouse’s occupation, primary diagnosis, length of residency in home, al-
cohol and prescription drug use, home ownership, and living arrange
-
ment.
The dependent variable, life satisfaction, was measured using the LSI-Z
(Wood, Wylie, & Sheafor, 1969). The LSI-Z is a shorter form of the
LSI-A (Neugarten, Havighurts, & Tobin, 1961). The LSI-Z contains 14
items that respondents rate agree, disagree,oruncertain. Possible total
scores range between 1 and 14 with higher scores indicating higher life
satisfaction. The LSI-Z is a self-report measure that has been normed on
100 elderly subjects with a mean life satisfaction score of 11.6 and a stan
-
dard deviation of 4.4 (Sauer & Warland, 1982). The LSI-Z has a
Kuder-Richardson reliability
1
coefficient of .79.
The Iowa Self-Assessment Inventory (Morris & Buckwalter, 1988) is

56-item scale that consists of seven subscales including economic re
-
sources, emotional balance, physical health, trusting others, mobility,
cognitive status, and social support. Items are rated on a scale from 1 (usu
-
8 JOURNAL OF GERONTOLOGICAL SOCIAL WORK
ally or always true) to 4 (usually or always false). The scores for each item
are summed to comprise a score that ranges from 8 to 32. This inventory
primarily has been normed on adults 65+ years old (Morris, Buckwalter,
Cleary, Gilmer, & Andrews, 1992). The internal consistency reliability
coefficients for the seven subscales range from .74 to .86 (Morris,
Buckwalter, Cleary, Gilmer, Hatz, & Studer, 1990). Construct validity has
been shown between each subscale and similar measures (Morris,
Buckwalter, Cleary, Gilmer, Hatz, & Studer, 1989).
The Geriatric Scale of Recent Life Events (Kiyak, Liang, & Kahana,
1976) is a 55-item scale that measures the number of life events that have
occurred within the previous three years. Subjects circle all events that
they have experienced, and the number of events circled is summed to
comprise a total score. Item examples include: “Death of a Close Friend”;
“Minor Illness”; “Gain a new family member”; and “Grandchild mar
-
ried.” This scale was normed on 248 individuals 60+ years old and has
shown good concurrent validity (.51 to .84) (Kiyak, Liang, & Kahana,
1976). The analysis reported here was based on a subscale of negative
events constructed for the study. It included 32 items.
The Multidimensional Health Locus of Control Scale (MHLC) (Wallston,
Wallston, & DeVellis, 1978) is an 18-item instrument that rates respon-
dents according to internal health locus of control (IHLC), powerful oth-
ers health locus of control (PHLC), and chance health locus of control
(CHLC). Respondents answer questions on a 4-point, Likert-type scale (1

= strongly disagree to4=strongly agree). Scores on each subscale are
summed, and higher scores indicate more external beliefs in locus of con-
trol. Typical questions include: “No matter what I do, if I am going to get
sick, I will get sick” and “Most things that affect my health happen to me
by accident” (Wallston et al., 1978). Inter-item reliability has been esti
-
mated to range from .67 to .86. Concurrent validity with similar locus of
control measures has been estimated to range from .51 to .73. This scale
was normed on the general population, with a median age range from 35 to
44 years.
The Index of Activities of Daily Living (ADL) (Katz, Ford, Moskowitz,
Jackson, & Jaffee, 1963) is a widely used measure that assesses a person’s
ability to carry out daily tasks such as walking, getting out of bed, climb
-
ing stairs, grooming, bathing, dressing, toileting, and feeding. Items are
rated “yes” or “no” in terms of dependence or independence for each ac
-
tivity. This index has shown good interrater reliability, as well as strong
correlations with measures of mobility and house confinement (Kane &
Kane, 1981).
Abu-Bader, Rogers, and Barusch 9
Finally, perceived health in general was measured by a 5-point Likert
scale item “In general, would you say your health is excellent, very good,
good, fair, or poor.”
Data Analysis
Two multiple regression methods, hierarchical and stepwise methods,
were conducted to determine which psychosocial measures were signifi
-
cantly associated with life satisfaction among respondents. Measures that
have shown significant correlations (p < .05) with life satisfaction were

entered in the regression equation. These variables were number of nega
-
tive life events, emotional balance, physical health, cognitive status, so
-
cial support, powerful others locus of control, and perceived health in
general. The dependent variable was life satisfaction, as measured by the
LSI-Z.
Prior to these analyses, frequencies and histograms were generated for
all variables to assess distributions and outlying cases. All variables were
normally distributed and had no outliers. For the regression analysis, diag-
nostics were performed to ensure multivariate assumptions were met.
Bivariate correlation matrices, variance inflation factor (VIF) values, and
tolerance criteria indicated no multicollinearity among the independent
variables.
FINDINGS
Descriptive Findings
Life Satisfaction. To describe the life satisfaction of participants in this
study, we computed descriptive statistics using the dependent variable,
life satisfaction. The mean score on the Life Satisfaction Index was 9.6
(SD = 2.5), slightly below the cutoff score (11.6) for a normal population
of elderly as reported by Sauer and Warland (1982). Scores on the life sat
-
isfaction ranged from 3 to 14, with 39% of participants reporting a score of
11 or higher (61% below the cutoff score).
Cognitive Status. Cognitive status was gauged using the Mini Mental
State Exam, as well as the cognitive status sub-scale from the Iowa
Self-Assessment Inventory. The mean score on the Mini Mental State Ex
-
amination was 25.8, with a range from 13 to 30. Folstein, Folstein, and
McHugh (1975), suggest using a criterion of 21 or less to gauge cognitive

impairment. Using this cut-off, only 14% of respondents showed signifi
-
10 JOURNAL OF GERONTOLOGICAL SOCIAL WORK
cant cognitive impairment. Further evidence of cognitive capacity was
provided by the cognitive status subscale from the Iowa Self-Assessment
Inventory. The mean score on this measure was 21.7, with a range from
8-32.
Locus of Control. Participants in this study showed a clear tendency to
-
ward external causal attributions. Their mean score on the Internal Locus
of Control sub-scale was 5.6, with a range from 2 to 8. The mean score on
external (“powerful others”) sub-scale was 14.7, with a range from 6 to
24. Respondents’ mean on the chance sub-scale was 12.4, with a range
from 6 to 19. Mean scores obtained when this instrument was normed
were 25.1 on the Internal Locus of Control sub-scale; 19.9 on the Powerful
Others sub-scale, and 15.6 on the chance sub-scale (Wallston et al., 1978).
Table 1 displays results for these descriptive analyses.
Life Events. The average number of negative life events participants ex
-
perienced in the year prior to this study was 7.5, with a range from 2 to 17.
The most common event reported was difficulty walking, experienced by
85% of the sample. This was followed by minor illness (84%), reduced
recreation (76%), illness of a family member (60%), hearing and vision
problems (56%), and less church activity (49%). Nearly half (48%) of the
sample had experienced death of a family member. Table 2 displays the
negative life events included in this study.
Predicting Life Satisfaction
Hierarchical and stepwise multiple regression methods were conducted
to estimate a model predicting life satisfaction. As was previously men-
tioned, variables that were significantly correlated with life satisfaction

were entered in the regression equation. Table 3 presents the correlations
between the dependent variable (life satisfaction) and the independent
measures.
The results of both hierarchical and stepwise multiple regression
methods were consistent, and therefore, the results of the stepwise are
reported in this study. These results are presented in Table 4. These re
-
sults show that life satisfaction is a function of physical health (beta =
.26, p < .0001), social support (beta = .19, p = .007), emotional balance
(beta = .34, p = .039), and powerful others locus of control (beta = .28, p =
.003). The results show that physical health has the strongest contribution
to the variance of life satisfaction. It contributes 14% of the variance in life
satisfaction, while each one of the other variables contributes 6% of the
variance. All four variables combined contribute 32% (R = .57) of the total
variance of life satisfaction.
Abu-Bader, Rogers, and Barusch 11
DISCUSSION
This sample of frail elders reported levels of life satisfaction that were
somewhat lower than those observed in studies of more healthy elders. In
this study, the mean score of life satisfaction (9.6) was slightly below
scores reported in studies of healthy seniors. In these studies, mean life
satisfaction scores have ranged from a low of 11.6 to a high of 15.39
(Kahana et al., 1995; Wood, Wylie, & Sheafor, 1969; Rao & Rao, 1981;
Gray, Ventis, & Hayslip, 1992; Adams, 1969). This difference is small,
and a significant proportion of respondents in this study reported levels of
satisfaction that were well within the range of those reported by more
healthy elders. Indeed, these results underscore what practitioners in the
field already know. Namely, that not all frail elders experience low life
satisfaction. In this sample, nearly half reported high scores on this mea
-

sure.
It is tempting to attribute the sample’s lower mean life satisfaction to
health and functional limitations. But results of the multivariate analysis
do not support this interpretation. The subjective measure, perceived
physical health was an important predictor of life satisfaction, whereas
more objective health measures were not. In bivariate analyses reported in
Table 3, more objective measures of functional ability (IADL and ADL)
12 JOURNAL OF GERONTOLOGICAL SOCIAL WORK
TABLE 1. Respondents’ Cognitive and Emotional Status (N
= 99)
Variable Mean Median SD Range
Life Satisfaction 9.6 10.0 2.5 3-14
Physical Health 15.4 14.0 4.7 7-26
Economic Resources 22.5 22.0 6.0 5-32
Emotional Balance 23.2 24.0 6.2 10-32
Trusting Others 28.1 29.0 4.3 13-32
Mobility 16.0 16.0 5.1 5-30
Cognitive Status 21.7 22.0 5.6 8-32
Social Support 27.3 29.0 5.4 10-32
Activities of Daily Living 2.6 3.0 1.8 0-8
Powerful Others Locus of Control 14.7 15.0 3.4 6-24
Internal Health Locus of Control 5.6 6.0 1.4 2-8
Chance Health Locus of Control 12.4 13.0 3.3 6-19
did not show a significant association with life satisfaction. In contrast,
personal health appraisal was significant in the bivariate analysis (r = .38).
Further, the measure was the most important predictor in our model pre
-
dicting life satisfaction. This is consistent with findings of other studies
(e.g., George, 1993; Henderson et al., 1993) that indicate that subjective
perception may be a better predictor of life satisfaction than actual func

-
tional ability. Clearly, apart from more objective measures, an individ
-
ual’s perception regarding his or her health is an important correlate of life
Abu-Bader, Rogers, and Barusch 13
TABLE 2. Negative Life Events (N
= 99)
Event Number Reporting % of Sample
Difficulty Walking 84 85
Minor Illness 83 84
Reduced Recreation 75 76
Family Member Ill 59 60
Hearing/Vision Problems 55 56
Less Church Activity 48 49
Death of Friend 47 48
Death of Family Member 45 46
Major Illness 45 46
Financial Difficulty 36 36
Stopped Driving 26 26
Friends Turned Away 15 15
Victim of Crime 15 15
Loss of Possessions 14 14
Moved into Home for Aged 13 13
Trouble with Children 12 12
Trouble with Neighbor 11 11
Age Discrimination 9 9
Took Large Loan 8 8
Sexual Difficulty 8 8
Argued with Spouse 6 6
Divorce 3 3

Death of Spouse 3 3
Legal Violation 3 3
Separation 2 2
Unfaithful Spouse 1 1
satisfaction. Practitioners who work with the frail elderly may find that
perceived health status serves as a proxy for other measures of well-being.
Thus any assessment of this population should include this parsimonious
measure.
Because this study is correlational, it is unclear whether results have
identified factors that cause life satisfaction. Findings mirrored those of
14 JOURNAL OF GERONTOLOGICAL SOCIAL WORK
TABLE 3. Correlations Between Life Satisfaction and the Independent Mea
-
sures (N
= 99)
Variable r
Physical Health .38**
Emotional Balance .34**
Social Support .31**
Negative Recent Life Events 2.26*
Cognitive Status .20*
Powerful Others Locus of Control .20*
Instrumental Activities of Daily Living (IADLs) .13
Trusting Others .13
Internal Health Locus of Control .12
Activities of Daily Livings (ADLs) 2.07
Chance Health Locus of Control .05
Mobility .05
Economic Resources .02
*p < .05

**p < .001
TABLE 4. Predicting Life Satisfaction
Variable R R
2
beta SE t p F p
Physical Health .38 .14 .26 .05 2.79 .006 15.69 .000
Social Support .45 .20 .19 .04 2.10 .039 12.12 .000
Emotional Balance .51 .26 .34 .04 3.50 .001 10.78 .000
Powerful Others Locus of Control .57 .32* .28 .07 3.03 .003 11.08 .000
Adjusted R
2
= .30
other studies in the important role of social support, emotional balance,
and powerful others locus of control in the life satisfaction of the frail el
-
derly. Clearly, as suggested by the results of multiple regression, frail el
-
ders who perceive their health as poor, who have limited social supports,
and whose emotional status is fragile should be considered likely candi
-
dates for low life satisfaction.
This study affords some practical implications for professionals com
-
mitted to enhancing the quality of life of frail elders. First, it is important
that assessments include a simple measure of perceived physical health.
This is an efficient way to appraise, not only physical well-being, but
also life satisfaction and possibly emotional status as well. Second,
while it is unclear whether life satisfaction is amenable to clinical inter
-
vention, efforts to enhance the quality of life for frail elders would do

well to consider the Life Satisfaction Index a possible evaluation mea
-
sure as one most likely to reflect the overall success of their efforts.
Finally, in illustrating the importance of diverse factors in predicting life
satisfaction this study underscores the importance of holistic intervention
that addresses not only personal traits and perceptions, but also social sup-
port and resources.
NOTE
1. For more information about Kuder-Richardson Reliability see Crocker and Algina
(1986).
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