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The Simple School Belonging Scale
The Simple School Belonging Scale: Working towards a unidimensional measure of student
belonging
By
Erin Feinauer Whiting
Brigham Young University
Department of Teacher Education
and
Kimberlee Everson
Western Kentucky University
and
Erika Feinauer
Brigham Young University
Draft Submitted to Measurement and Evaluation in Counseling and Development
Published Online 2017
Full Citation: Whiting, E. F., Everson, K., & Feinauer, E. (in press). The
Simple School Belonging Scale: Working towards a unidimensional measure of
student belonging. Measurement and Evaluation in Counseling and
Development. DOI: doi.org/10.1080/07481756.2017.1358057
Link to 50 free copies: http://www.tandfonline.com/eprint/TqhrhKfsxKgAhv6ZJWrj/full
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The Simple School Belonging Scale
The Simple School Belonging Scale: Working towards a unidimensional measure of student
belonging
A student’s sense of belonging, and other closely associated constructs of school community,
have been shown to relate to a large variety of psychological, health-related, and academic factors in
school (Allen & Bowles, 2012; Anderman, 2003; Battistich, Solomon, Kim, Watson, & Schaps,
1995; CDC, 2009a; 2009b; Goodenow & Grady, 1993; Libbey, 2007; MacNeil, Prater & Busch,
2009; Osterman, 2000; Sergiovanni, 1994; Solomon, Watson, Battistich et al, 1996; Voelkl, 2012;
Wingspread, 2004). Conversely, for all students, a lack of school belonging is associated with
loneliness, emotional distress, psychosocial disturbance, suicide, mental illness, and depression
(Allen & Bowles, 2012). School connectedness and belonging has been found to be second only to
family connection in protecting children and adolescents against emotional distress, eating disorders,
and suicide (CDC, 2009a; 2009b). In fact, it has been suggested that connectedness to school is the
strongest protective factor in decreasing negative behaviors such as substance abuse, school
absenteeism, early sexual involvement, and violence for both boys and girls in 7th through 12th grades
(CDC, 2009b; see also Resnick, Bearman, Blume et al, 1997).
School transitions are periods of heightened physical and emotional upheaval for students
(Harter, Whitesell, & Kowalski, 1992) and can interfere with developing a sense of belonging in the
school community. This is especially marked for students transitioning out of elementary schools to
middle school or junior high school who are also experiencing a transition to adolescence, which can
be emotionally disorienting and uncomfortable (Eccles & Roeser, 2010). Middle schools or junior
high schools typically combine students from several elementary schools. They are larger and often
contain a more diverse student body (Eccles & Roeser, 2010). The organization of the school day is
also new, with classes changing every 45-50 minutes, requiring students to adjust to a setting that
requires more organizational skills, increased levels of independence and self-governing, as well as
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The Simple School Belonging Scale
increased demands for social awareness (Midgely, Anderman, & Hicks, 1995). Navigating this new
setting includes having multiple teachers and more complex peer interactions throughout the day
(Eccles & Roeser, 2010; Benner, 2011; Wigfield & Wagner 2005). For students at this transition to
the secondary education school environment, school often includes changes in friendships and peer
groups, and can feel impersonal and isolating for many students negatively impacting their sense of
belonging at school (Benner, 2011). This critical stage in schooling provides an interesting and
constructive setting for examining school belonging and the measurement of belonging.
School belonging has been measured in various ways across school settings and age ranges. For
example, Libbey (2004) found that although many scholars acknowledge the importance of belonging
for students and schools, there is a lack of consistency in how this construct is defined and
operationalized in research. She found more than 21 different measures of belonging in an extensive
review of literature on belonging in schools. In fact, many of the related constructs in the literature,
which include school bonding, attachment, relatedness, membership, and others, use similar wording
in their items and scales (Libbey, 2004). Despite this conceptual inconsistency, the Psychological
Sense of School Membership (PSSM, Goodenow, 1993) scale was developed in middle schools for
the use of researchers and school practitioners and has been widely used in research examining
belonging and feeling connectedness to school for students in middle and high schools.
Previous studies using the PSSM have found a sense of belonging or connectedness to
positively correlate with school success and motivation (Goodenow, 1993; McMahon, Parnes, Keys,
& Viola, 2008). Research also has found moderate correlations with better school attendance
(Sanchez, Colon, & Esparza, 2005), academic self-efficacy (Ibanez, Kuperminc, Jurkovic, & Perilla,
2004; Gutman & Midgley, 2000), and GPA (Anderman, 2003; Booker, 2007; Gutman & Midgley,
2000). Additionally, negative relationships have been found between the PSSM scores and scores on
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The Simple School Belonging Scale
the Child Depression Index (Shochet, Dadds, Ham, & Montague, 2006). Increased feelings of school
connectedness, as measured by the PSSM, have been found to be related to lower levels of anxiety
(McMahon et al., 2008).
The PSSM was developed by Carol Goodenow (1993) to examine student perceptions of
belonging as it relates to academic motivation in school. She defines the construct measured by the
scale as the “extent to which students feel personally accepted, respected, included and supported by
others in the school environment” (1993, p.80). Forty-two items were initially constructed focusing
on perceptions of liking, personal inclusion, acceptance, respect and encouragement as well as more
general sense of belonging (Goodenow, 1993). These were paired down to 28 before administering
the scale in middle school and junior high school settings. Initially, one third of the questions were
purposefully phrased in a negative direction, and all questions used a 5-point Likert scale (true- not
true)(Goodenow, 1993). Her 18-item measure was developed by removing items that contributed to
low score reliability and exhibited minimal response variance (Goodenow, 1993; You et al, 2011).
Recent research reveals more than 42 studies using the PSSM with an additional 213
references to this scale (You, Ritchey, Furlong, Shochet & Boman, 2011). However only 27 of these
studies use the full 18-question scale as developed by Goodenow (1993) and there are concerns about
the level of inconsistency in the literature in how it is interpreted and used across these studies (You
et al, 2011). As You and associates (2001) note, the PSSM is almost always used as a unidimensional
measure despite conflicting psychometric evidence of its dimensional structure.Uses of the PSSM,
largely as a unidimensional construct, have been helpful for raising questions about the importance of
belonging in schools. Further, Ye and Wallace (2014) argue, “Having a psychometrically sound
measure of students’ sense of school belonging permits future intervention-based work in schools” (p.
213) and suggest that such a scale might be helpful in identifying students who need additional
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The Simple School Belonging Scale
support or in monitoring teacher effectiveness. In practice, a clear unidimensional scale of school
belonging with strong psychometric properties would be of value to the field. However, it has been
difficult to find consensus on the appropriate use of the PSSM as a unidimensional approach to
measure school belonging.
Recent research indicates that the PSSM scale is multi-dimensional with debate in the
literature as to both the structure and interpretation of the factors (Cheung & Hui, 2003; Cheung,
2004; Harborg, 1994; 1998; O’Farrell & Morrison, 2003; Ye &Wallace, 2014; You et al, 2011).
Because the PSSM was originally developed as a unidimensional scale, it is not always clear how it is
best adapted to be able to use it as such. Scholars have variously dropped items problematic for
unidimensional use and in efforts to improve psychometric properties (Anderman, 2003; Gutman &
Midgely, 2000; Hagborg, 1994; Hagborg, 1998) or borrowed a few questions to add and compliment
other related items (Voelkl, 1996) but there is not a systematic and agreed upon adaptation for use.
Additionally, there is variability in the resulting factor structures of the PSSM tested in previous
research.
A few notable studies have focused on understanding and unpacking the multidimentionality of
the PSSM in an effort to more clearly define school belonging as measured by this scale. Hagborg
(1994) first raised questions about the PSSM scale reflecting a unidimensional construct, and
attempted to identify subcomponents through a principal components analysis. He identified a three-
factor solution, including the dimensions belonging, rejection, and acceptance. However, he was
unable to identify clear distinctions between the separate dimensions of the scale because of cross-
loadings across factors. As a result he recommended reducing the full 18-item measure because of
these cross loadings to a modified 11-item unidimensional scale (Hagborg, 1994; Hagborg, 1998)
rather than pursuing a three-dimensional understanding of school belonging. Similarly, Cheung and
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The Simple School Belonging Scale
Hui (2003; Cheung, 2004) conducted a principal components analysis on a Chinese version of the
PSSM and identified a two-factor solution, comprising of the dimensions school belonging (13 items)
and feelings of rejection (5 items).
You and associates (2011) examined the factor structure of the PSSM using both exploratory
and confirmatory factor analyses using split-half random samples. These authors identified a three-
factor solution, comprised of the factors they called caring relationships, acceptance, and rejection,
and eliminated the possibility of a hierarchical structure with one higher order factor. In line with
other work with the PSSM, these authors found that many items cross-loaded across factors. However
their recommendation was a reduction of items from 18 to 12 retaining all three factors. Likewise, Ye
and Wallace (2014) conducted Exploratory Factor Analysis (EFA) and Confirmatory Factor Analyses
(CFA). These authors discovered a four-factor solution, including three substantive factors and a
method factor. Three items that either cross-loaded on the three substantive factors or had weak
loadings were eliminated from the scale. Ye and Wallace (2014) labeled the substantive factors as
identification and participation in school (6 items), perception of fitting in among peers (5 items),
and generalized connection to teachers (4 items). Additionally, they identified a method factor,
which included all of the negatively worded items (5 items) which were also found to cross-load on
every other factor. These authors argue that this fourth factor is a method factor rather than a true
rejection factor identified in other studies. They argue that a true rejection factor should exist across
domains and contexts, which is not the case in the negatively worded items on the PSSM reflected in
this factor. They further conclude that the rejection factor identified by other authors is most likely
simply a method effect.
Finally, O’Farrell and Morrison (2003) found that all but five items on the PSSM cross-loaded
onto other scales through an exploratory factor analysis of the PSSM along with several other scales
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The Simple School Belonging Scale
related to school bonding. These authors suggest that only five items on the PSSM represent
something unique and assert that the construct of school belonging or bonding is indeed complex.
Clearly constructs related to school belonging must be clearly articulated and discretely measured in
order to be useful for stakeholders seeking to improve student experiences.
[Insert Table 1 about here]
From the above reviewed studies, we see the varying and sometimes conflicting ways in
which the PSSM has been shown to measure sense of belonging in schools (see Table 1), which has
led to some confusion about the underlying conceptualization of the construct. You and associates
(2011) assert that much more work needs to be done to understand the factor structure of the PSSM in
order to resolve inconsistencies among studies. The lack of clarity has led to further questions about
the overall continued usefulness of the PSSM as the primary measure used by scholars measuring
students’ sense of belonging at their school, especially when used in a unidimensional application.
Although a multidimensional model of school belonging is clearly important and warrants continued
investigation, unidimentional uses of available measures (such as the PSSM) also suggests the
practical importance of having a reliable and validated simple scale as a starting point for scholars
examining school belonging.
The current study again examines the factor structure of the PSSM in one sample and then
presents work toward the construction and psychometric analysis of a new unidimensional measure of
belonging that we have called the Simple School Belonging Scale (SSBS). The goal of this project is
to return to efforts in the development of a strong unidimensional scale of school belonging, using the
PSSM as a place to start, in order to have a reliable and practical scale for both research scholars and
school practitioners. In this paper we examine the overall structure of the PSSM with our sample in
Phase 1, we explore the potential of a new unidimensional belonging scale using the PSSM with the
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The Simple School Belonging Scale
addition of new items in Phase 2, and validate and examine the psychometric properties of data for
this new unidimensional belonging scale in Phase 3.
Method
Participants
This project is part of an ongoing collaboration with one junior high school, including grades
7, 8 and 9, located in the intermountain region of the United States. Approximately 900 students were
surveyed about their school experiences at the beginning and end of the school year for 3 consecutive
years. This school is the only middle level school in the town and represents a cross section of the
overall population. A majority of students are White European American and speak English as a first
language, however about 16% of the school population identify as Hispanic or Latino. Additionally,
about 39.5% of students participate in the national free and reduced lunch program at this school.
This sample, like others used to look at the PSSM factor structure, is a convenience sample and
therefore limited in some ways. However, as all students at this school participated in the survey our
sample represents the population of this particular community and school. As previous work with
convenience samples shows various outcomes in the factor structure of the PSSM, we begin by
looking at the factor structure in our own sample to place our work in context and continue to explore
these factor variations.
Data Collection
In the spring of 2013, a 45-minute survey was administered to all students through an online
survey program in the computer lab during school. As part of this survey students answered questions
taken from the Vaux Social Support Record (VSSR, Vaux et al, 1986), a nine-item index of social
support adapted from the original 23-item Social Support Appraisals scale (SS-A, Vaux et al, 1986),
and the full PSSM scale (Goodenow, 1993). In addition to the PSSM, fourteen additional items
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The Simple School Belonging Scale
related to the construct of school belonging were included in the survey. The intent in adding
additional items was to modify and extend the PSSM to create a reliable unidimensional scale that
effectively measured school belonging. In order to accomplish this, a pool of additional questions
were developed by the authors from a review of literature and research on belonging. We followed
recommendations by Worthington and Whittaker (2006) who recommend an expert review of a
limited number of items for content validity during scale development stage. They recommend very
limited, if any, construct validity work (convergent, discriminant) at this development stage and argue
that it is best to keep the questionnaire short and central to the purpose as other items may “interact”
with the items being tested and affect response patterns on the critical items that are being tested in
this stage. We selected these 14 items after a review by a panel of scholars for content validity and
clarity, sensitive to the limitations of space in the survey. These were placed as a separate set of items
in the survey along with the PSSM and the VSSR. Various demographic student data was also
gathered from the survey and from the school.
We adopted a four-point likert scale (“NO!,” “no,” “yes,” “YES!”) after considering research
arguing for and against the use of a middle response category in Likert type scales (e.g., Clark &
Watson, 1995; Krosnick, Holbrook, Berent, Carson, Hanemann, Kopp, et al, 2002; Nowlis, Kahn, &
Dhar, 2002). Research indicates that middle response categories can be inconsistent, reflecting
situational endorsements and can be indications of ambivalence, confusion or a form of nonresponse
(Kulas & Stachowski, 2013; Hernández, Drasgow, & González-Romá, 2004). Further, prior studies
have used a four-point scale with adolescents (CDC, 2014). Thus, after consultation with the school
administration and counselors at the school, we deemed it appropriate for our purposes with this
population and age group for these measures.
Data Analysis
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The Simple School Belonging Scale
The goal of the first phase of analyses in this study was to replicate the findings from prior
scholars using exploratory and confirmatory factor analyses (CFA). Based on preliminary findings
from these analyses, we then explored alternative structures to the PSSM based on our sample. The
goal of Phase 2 of our analysis was to use the additional information contained in the 14 new
belonging items to both better understand the structure of the PSSM and to identify a supportable
unidimensional adaptation of a belonging scale. To this end, we repeated these EFA and CFA
analyses with the addition of the additional 14 new belonging items to the PSSM questions. Given the
history of using the PSSM as a one-dimensional measure of belonging, our goal of this phase was to
develop a more psychometrically sound unidimensional belonging scale. In Phase 3 we examined the
scale developed in Phase 2 for item difficulty, item and test information, and item discrimination
statistics in order to better understand the adequacy of the scale.
Procedures. To begin our analyses in Phase 1, the overall sample was randomly split into two
subsamples. Sample A comprised the development sample, and Sample B the validation sample. The
881 students included in the spring 2013 panel were randomly split into two groups for analysis.
Sample A included 392 students and Sample B included 465 students. Males consisted of 47.8% of
the students in Sample A and 50.9% in Sample B. Students with free or reduced lunch status included
37.5% of the students in Sample A and 44.5% in Sample B. In Sample A, 80.3% students identified
as white and in Sample B 77.7% identified as white. 9.2% of the students in Sample A identified
Spanish as their dominant language and 7.7% in Sample B. Sample A included 127 seventh graders,
126 eighth graders, and 139 ninth graders compared to 144 seventh graders, 165 eighth graders, and
154 ninth graders in Sample B. On average, the students in Sample A had lived in the local
community for 9.18 years (SD = 4.66) while the students in Sample B had lived in the community for
9.27 years (SD = 4.64).
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The Simple School Belonging Scale
For Phase 1 and Phase 2, a hypothesized structure of belonging was identified using EFA with
the development sample (Sample A), including possible item deletions. We began with EFA because
the variety of structures uncovered by prior studies left us unsure as to whether any prior discovered
structure, or something entirely new, might be discovered in our sample. The final hypothesized
structure resulting from EFA was tested in the validation sample (Sample B) using CFA. Although
similar analyses were performed in both Phase 1 and Phase 2 of our study Phase 2 includes new items
in addition to the PSSM that are analyzed in Phase 1.
A WLSMV (robust weighted least squares) estimator was used in MPLUS for both the EFA
and CFA analyses due to the fact that normality could not reasonably be assumed (Brown, 2006;
Muthen & Muthen, 1998-2001). For both EFA and CFA analyses, model fit was examined using the
root mean square error of approximation (RMSEA), the Comparative Fit Index (CFI), and the Tucker
Lewis coefficient (TLI). The RMSEA was considered acceptable if its confidence limits included
0.08 and was considered to be good if they included 0.05, with values closer to zero representing
better fit. The CFI and TLI were considered to indicate good fit if they were above 0.95, and marginal
fit if between .90 and .95, which is in accordance with current standards for these fit statistics
(Bandalos & Finney, 2010; Brown, 2006). However, we chose to interpret these criteria as guidelines
rather than as firm rules (Worthington & Whittaker, 2006).
In examining items with large cross-loadings, we followed the advice of Worthington and
Whittaker (2006) and determined a priori a threshold that would be consistently used for determining
whether cross-loadings suggested item removal. In keeping with their suggestion that that threshold
be set as low as possible provided reliability and validity do not suffer, we used a threshold of .20,
with the understanding that we would increase that threshold if needed. This threshold partly reflected
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The Simple School Belonging Scale
our preference for a shorter scale with approximate simple structure, if possible, in order to maximize
usefulness to practitioners and also reduce survey burden when the scale was used in future studies.
Phase 3 analyses were conducted to investigate the psychometric properties and to verify the
new belonging scale specified in Phase 2. These analyses were conducted in R software (R Core
Team, 2014) using the grm function, an estimator based on Samejima’s graded response model
(1969), in the ltm package (Rizopoulos, 2006). This function uses an approximate marginal maximum
likelihood estimation approach. Because sample size requirements are large for polytomous scales,
the entire sample (N = 857) was used for these item response theory-based analyses. A minimum
sample size of 500, with 1000 or more preferred, is considered appropriate for graded response
models (Reise & Yu, 1990). Our purpose, however, was to examine item quality, not to calibrate
particular items, making a split sample less necessary for the IRT analyses. Category response and
information curves were examined for apparent usefulness of the item categories, coverage of the
intended range of the trait, and appropriate discrimination at various levels of the trait. As part of
Phase 3, evidence of construct validity was established by correlating our new unidimensional
belonging scale to the Vaux Social Support Record (Vaux et al, 1986) with the expectation that the
two scales would be strongly, but not perfectly, correlated. Additional construct validity was
established by correlating the scale with the number of years the student had resided in the local
community. This relationship was expected to be weak, but significant and positive.
Results
Phase 1: PSSM Factor Structure
Exploratory factor analyses. Using Sample A, exploratory factor analyses were conducted in
MPLUS (Muthén & Muthén, 1998-2011) using the WLSMV estimator. Factors were rotated using an
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The Simple School Belonging Scale
oblique (Geomin) rotation, following Ye and Wallace (2014). Results comparing 2 and 3 factor
models using Sample A are presented in this section.
An examination of eigen-values (λ1 = 9.01, λ2 = 2.11, λ3 = 1.21, λ4 = 0.81) in the EFA initially
suggested a three-factor solution using either the oft-used λ = 1.0 cutoff, examination of scree plots,
and parallel analysis. In the two-factor model, we found inadequate fit (χ2 = 757.41, df = 118, p =
0.000, CFI = .933, TLI = .913, RMSEA = .118). The three-factor model fit noticeably better (χ2 =
496.92, df = 102, p = 0.000, CFI = .959, TLI = .938, RMSEA = .100) with a chi-square difference test
showing statistical significance (Δχ2 = 260.49, Δdf = 16, p < .001), however the RMSEA was still
unacceptably high, as the confidence interval [.091, .109] did not contain even the most liberally
accepted value of .08. The CFI and TLI fit statistics for the 3-factor model, however, indicated good
and adequate model fit respectively. In spite of findings from Ye and Wallace’s (2014) study pointing
to a four-factor model, the Eigen-values from these data provided no justification for a four factor
model in our analyses.
Examination of factor loadings for the three-factor model (Table 2), suggested the majority of
items (13) loaded on the first factor and the other 5 loaded on the second factor. This division is
aligned cleanly with the positive versus negative wording of the items. Unlike Ye and Wallace’s
(2014) finding, only one of the negative items is cross-loaded on another factor suggesting little
evidence of a method effect. The third factor includes at least three items, but the factor loadings are
mostly under 0.50. Thus, the third factor appears to be weakly defined. In addition, all of the items
loading on this factor are cross-loaded onto one of the other factors, with cross-loadings of at
least .554. In fact, only one item from Factor 3 does not cross-load with Factor 1. Thus factor 3 does
not appear to represent a factor that is clearly distinguishable from the others. Correlations among the
factors are included in Table 3.
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The Simple School Belonging Scale
[Insert Table 2 about here]
[Insert Table 3 about here]
As our goal is to identify independent factors of belonging, one possibility suggested by our
EFA was to eliminate all items that loaded on the ill-defined third factor, and accept a reduced two-
factor instrument. In this scenario, if the six items with loadings on Factor 3 greater than 0.20 are
eliminated, eight items remain to measure Factor 1 and four items remain to measure Factor 2. We re-
ran the EFA with items 4, 5, 7, 9, 14, and 15 removed and only allowing two factors. Fit statistics
were mixed (χ2 = 278.95, df = 43, p = 0.000, CFI = .963, TLI = .943, RMSEA = .119, Upper limit =
0.132, Lower limit = 0.106). Factors were strongly correlated (r = .53). We conclude, however, that a
2-factor reduced model is the best fit for the PSSM in Sample A and proceed with a CFA to confirm
the model.
Confirmatory factor analyses. In order to validate the findings of a two-factor, 12-item
model suggested by the exploratory factor analyses in Sample A, a CFA was conducted using our
validation sample, Sample B. All factor loadings were moderate to strong (above 0.50) and
statistically significant as shown in Table 2. The factor correlation was high (r = -0.71) suggesting
that the positive and negatively worded items may only be distinguished due to a method effect. Fit
statistics, however, were inconsistent in reflecting even adequate model fit (χ2 = 433.30, df = 53, p =
0.000, CFI = .942, TLI = .928, RMSEA = .125, Upper limit = 0.136, Lower limit = 0.114).
Modification indices suggest a large number of potential error covariances or factor cross-loadings.
The model was not modified, however, as the purpose of the CFA was model validation, not
exploration, and model modifications at this stage were likely to capitalize on chance.
In addition, we estimated the model with negatively worded items as a method effect
(correlated covariances) rather than as a second factor. Model fit using this approach was slightly
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The Simple School Belonging Scale
better than when fitting a two factor model, but reached good fit standard for only the CFI fit statistic
(χ2 = 345.43, df = 48, p = 0.000, CFI = .955, TLI = .938, RMSEA = .116, Upper limit = 0.104, Lower
limit = 0.127).
Our results in Phase 1 indicate that the PSSM is not a unidimensional measure of belonging
and does not have good fit as a two-factor model even after eliminating cross loading items. This is in
line with previous work in other samples (Cheung & Hui, 2003; Cheung, 2004; Hagborg, 1994; 1998;
O’Farrell & Morrison, 2003; Ye & Wallace, 2014; You et al, 2011), although we found differences
across the development (Sample A) and validation (Sample B) samples in our own analysis of the
structure of this measure.
In sum, our findings differ from previous scholars in that our analysis pointed to a two-factor
model after removing the six items that loaded onto an unspecifiable third factor. Following Ye and
Wallace (2014), we also explored the possibility that the third factor represented a method effect due
to the negative wording of the items. However, unlike Ye and Wallace, we did not find that all
negatively worded items were cross-loaded with other factors, suggesting the possibility that the
feeling of rejection factor may indeed be a unique construct. As these authors suggest, however,
examining responses to these items on an instrument that contains items from a variety of scales may
help uncover whether these items represent only method effect or represent a substantive construct.
Despite the fact that the PSSM is often used as a unidimensional scale measuring belonging, our
findings suggest that this is an inappropriate use of this scale.
Phase 2: PSSM adding Additional Belonging Items
The goal of the second phase of this study was to determine whether the PSSM could be
improved as a measure of belonging with approximate simple structure with the addition of new
items. The following EFA and CFA analyses explore the development of an optimal unidimensional
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The Simple School Belonging Scale
belonging scale using the combined set of items from the PSSM and the 14 new items designed to
measure sense of belonging.
Exploratory Factor Analyses. As in Phase 1, EFAs were estimated in MPLUS using the
WLSMV estimator and Geomin rotation with Sample A. Eigen-values suggested a four-factor
solution when the additional items were included (λ1 = 16.43, λ2 = 3.05, λ3 = 1.68, λ4 = 1.34, λ5 =
0.95), but a three-factor solution was also estimated for comparison. The three-factor solution had
adequate fit on all measures (χ2 = 1563.62, df = 403, p = 0.000, CFI = .948, TLI = .937, RMSEA
= .086, Upper limit = .090, Lower limit = .081). However, the four-factor solution had excellent fit (χ2
= 1194.48, df = 374, p = 0.000, CFI = .964, TLI = .952, RMSEA = .075).
The pattern of factor loadings for the four-factor solution (Table 4) revealed many significant
cross-loadings. Factor 1 included most of the positively worded items and, as in Phase 1, Factor 2
included all the negatively worded items. The third factor in this model was constructed similarly to
the third factor found in Phase 1, when only items from the PSSM were included. In this model,
Factor 3 is more cohesive though still comprised of items only from the PSSM. The addition of the
new items appears to have clarified the factor structure, with many squared factor loadings above
0.50 and at least two of the items are measured without cross-loading on other factors. The fourth
factor is unique among the factors in that it includes a balance of positively and negatively worded
items. All of the factor four items, however, had cross-loadings on either Factor 1 or Factor 2 of at
least .578, making this factor independently uninterruptable. Interestingly, even following Ye and
Wallace’s (2014) approach where the factor representing negative items is considered a method
effect, considering Factor 4 as an independent factor remains problematic in our analyses. Factor
correlations are included in Table 5.
[Insert Table 4 about here]
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The Simple School Belonging Scale
[Insert Table 5 about here]
In sum, additional items were designed to represent the construct of school belonging and
included in the analyses in order to validate the constructs represented by the PSSM itself. We
uncovered a three-factor structure for our sample in our EFA. The first factor seemed best represented
by a factor we called school belonging, the feeling that a student feels comfortable, accepted, and
liked at the school. The second factor, feelings of rejection, included primarily the negative items.
However, significant negative loadings on the second factor in the EFA for the positively-worded
items “I can really be myself at this school” and “I fit in with other students at (school name)” may
provide evidence of a substantive rejection factor rather than a method effect. Cross-loadings,
however, muddy the interpretation of this factor and only two items, both negatively worded, were
identified to measure the factor during the CFA. Thus, this factor is underspecified and may not
validly represent the breadth of the construct. A third factor identified in the EFA, connection to
teachers, was also underspecified (two items) once cross-loaded items were removed for the CFA
analysis. While EFA suggested a fourth factor, school loyalty, which included both positively and
negatively worded items, all items were cross-loaded on other factors. Thus the school loyalty factor
cannot be measured as an independent construct. Among these four factors, then, only the school
belonging factor, indicated by ten items, is potentially fully specified.
Based on these exploratory analyses, two final approaches to modeling belonging from these
data emerged as options to be confirmed through CFA. The first approach considered included
eliminating all items that loaded strongly on the problematic Factor 4, with any other items with
significant cross-loadings also removed. This model would retain the ten items that loaded cleanly on
Factor 1, the two items that loaded cleanly on Factor 2, and the two items that loaded cleanly on
Factor 3. As noted above, this multidimensional approach raised question about the possibility of
17
The Simple School Belonging Scale
being fully specified. The second approach retains the ten items on Factor 1 and eliminates all other
items. This approach is in line with our overarching research goal, seeking to confirm a
unidimensional model of belonging.
Confirmatory Factor Analyses. Confirmatory factor analyses using Sample B revealed that
both approaches to the data that emerged from the EFA were viable models. A multifactor model was
found to have good fit (χ2 = 276.61, df = 74, p = 0.000, CFI = .975, TLI = .969, RMSEA = .077,
Upper Limit = .067, Lower Limit = .086), after dropping items from Factor 4 as suggested by the
EFA. The second approach, specifying a unifactor model, also was confirmed to have good fit. As
our goal in these analyses was to explore the feasibility of developing a robust unidimensional model
in order to advance the work of belonging among adolescent students, we present the results of this
second approach, the unifactor model, in this paper.
The ten-item unifactor model had good fit (χ2 = 150.50, df = 35, p = 0.000, CFI = .982, TLI
= .977, RMSEA = .084, Upper Limit = .098, Lower Limit = .071). Interestingly this factor included 5
items from the PSSM and 5 items from the new belonging questions added in Phase 2. All
standardized loadings were large (at least 0.635) and statistically significant (Table 5). The internal
consistency as measured by Cronbach’s alpha was 0.91 for the scores estimated using this unifactor
model. Using Raykov’s (2004) CFA-based method, the scale reliability of the scores was 0.96.
Phase 3: Item Response and Construct Validation of the Unidimensional Scale
The results of our confirmatory factor analysis in Phase 2 show that our 10-item one factor
model represents a robust unidimensional measure of student belonging. These encouraging results
led us to further test the psychometric properties of the scores in this new belonging scale through an
item response analysis and construct validation, which we carried out in Phase 3 of this study.
18
The Simple School Belonging Scale
Item Response Analysis. Using the graded response model (Samejima, 1969), the final
unidimensional factor model converged and reported a negative log likelihood of -7960.872 with AIC
= 16001.74 and BIC = 16192.11. These measures are most interpretable in comparing models, with
lower values representing better fit. Item parameter estimates indicate all items are discriminating
(discrimination parameters greater than 1.0), suggesting a much higher probability of selecting a
higher response category if the person has a greater sense of belonging. Thresholds for each item are
fairly evenly spaced and non-overlapping (Table 6) ), indicating all response categories are
functioning well with each category representing a higher degree of belonging. Item category
response curves (Figure 1) verify the distinct functioning of the response categories for this sample.
[Insert Table 6 about here]
[Insert Figure 1 about here]
In addition, item information curves (Figure 2) suggest that the items provide optimal
information(the item curves are peaked) about respondents with ability levels between -2 and 2 on
the scale. For our scale, 97.87% of respondents had factor scores in this ability range, as estimated by
the model. In essence, the IRT analysis suggests that the items individually extract helpful
information that allows for fine distinctions in the levels of belonging possessed by the respondents to
this survey.
[Insert Figure 2 about here]
Construct Validation. While we made significant efforts toward content validity we also
found some limited evidence of construct or criterion validity. The size of the loadings from the CFA
for the ten-item unidimensional school belonging scale as well as the reliability evidence suggest high
levels of factor cohesion. Using Sample B in MPLUS, evidence of construct validity was found
through correlating the new ten-item school belonging scale with the Vaux School Support Scale
19
The Simple School Belonging Scale
(1986). Although both scales had items measuring student perceptions of whether people at school
care and can help students at school in one form or another, items do not overlap in these two scales.
When both scales were included, the model had mediocre fit (χ2 = 1018.92, df = 103, p = 0.000, CFI
= .935, TLI = .924, RMSEA = .138, Upper Limit = .146, Lower Limit = .131). However the
correlation between the two constructs was r = 0.64, which aligns with expectations, suggesting some
evidence of construct validity. Model fit might be improved by adding error covariances within the
social support scale. However, we felt we had found adequate evidence of validity without making
revisions to the measurement of school support. The belonging scale correlated weakly with the
number of years the student had lived in the local community (r = 0.142, p = .007), as expected (see
also Gallagher, 1996). This provides some limited evidence of discriminant validity, however, much
more work related to validating this scale in in order. As we have exhausted the limits of this
particular data, future work with a new sample can extend this work and gather more evidence of
construct validity.
In sum, the scale tested in our analyses in Phase 3 that includes five PSSM items and five new
items, has strong psychometric properties, including high score reliability. These findings point to the
construction of a new, robust, unidimensional, measure of school belonging with minimal
measurement error. We have called this new measure the Simple School Belonging Scale (SSBS).
The development of this new scale is significant because it provides a unidimensional scale that can
be used to compare school belonging across groups and track change in school belonging for
individuals across time.
Discussion
Having a sense of belonging in school is protective for students and supports the psychosocial
and academic wellbeing of students. This is particularly interesting in middle level education during
20
The Simple School Belonging Scale
which time students are in a crucial transition time. Unfortunately, there has not been consensus in the
field on ways to conceptualize and measure student belonging. One commonly used measure has
been the PSSM, which has generally been applied unidimensionally and without much psychometric
substantiation. We argue that a unidimensional measure of student belonging in schools is warranted
to assist researchers and practitioners in intervention-based work and increase insight into helpful
approaches for student belonging (Ye &Wallace, 2014).
The main contribution from this study is the presentation of a new measure of school
belonging, the Simple School Belonging Scale (SSBS). The SSBS contains 10 items, 5 taken from the
PSSM and 5 from a set of new items collected for this study. Results from our analyses reveal that the
SSBS is psychometrically sound with preliminary evidence of construct validity. Interestingly, the
inclusion of these new belonging items also clarified the structure of the PSSM items in our
exploratory factor analyses.
Our study builds on the work by scholars who began to critique the PSSM in an effort to
improve the measurement of school belonging overall. This study extends the work of previous
scholars by developing and testing a new measure of belonging that is more appropriate for
unidimensional applications than previously used measures such as the PSSM. Although this is an
important contribution, it is just one step forward in conceptualizing and measuring school belonging
in more coherent and unified ways. Future research should attend to validation of the SSBS across
age groups and across varied contexts in order to continually advance the theoretical and
methodological underpinnings of student belonging.
The continued use of the PSSM as a unidimensional measure of belonging in research
suggests the usefulness and demand for a simple unidimensional scale. Indeed, there is much that can
be learned by examining an overall sense of belonging in schools with a simple reliable
21
The Simple School Belonging Scale
unidimensional tool. However, we should also acknowledge the difficulties revealed in work to
develop such a scale. Our work here has been interested in developing a psychometrically strong
unidimensional measure of belonging that can be consistently used by researchers and practitioners in
the field. Yet, we also recognize the overwhelming evidence of the complexity surrounding
measurement of school belonging that must be closely examined as we go forward. Although we did
not pursue further analysis due to our specific purpose in this study, our own work suggests that a
two-dimensional approach might also yield productive insight into the conceptual terrain of school
belonging. There is certainly much more work to be done in unpacking and further specifying
constructs related to belonging. We encourage future research to expand understandings of how
concepts of school belonging, connectedness, bonding, social support, and other related constructs
relate and differ from each other.
22
The Simple School Belonging Scale
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The Simple School Belonging Scale
Table 1
Factor identifications for the PSSM in prior studies
Item
Number Item
Hagborg
(1994)
Cheung & Hui
(2003)
You et al.
(2011)
Ye & Wallace
(2014)
1I feel like a real part of
(school name).
Belonging,
Acceptance
School
belonging Removed
Identification &
participation in
school
2People here notice when
I am good at something. Belonging School
belonging Acceptance Removed
3It is hard for people like
me to be accepted here. Rejection Feeling of
rejection Rejection Perception of fitting
in among peers
4
Other students in this
school take my opinions
seriously.
Belonging School
belonging Acceptance Perception of fitting
in among peers
5
Most teachers at this
school are interested in
me.
Belonging School
belonging
Caring
Relationships
Generalized
connection to
teachers
6Sometimes I don't feel as
if I belong here. Rejection Feeling of
rejection Rejection
Identification &
participation in
school
7
There's at least one
teacher or adult in this
school that I can talk to if
I have a problem.
Belonging School
belonging
Caring
Relationships
Generalized
connection to
teachers
8People at this school are
friendly to me. Belonging School
belonging Removed Perception of fitting
in among peers
9
Teachers here are not
interested in people like
me.
Belonging Feeling of
rejection
Caring
Relationships
Generalized
connection to
teachers
10 I am included in lots of
activities at this school. Belonging School
belonging Acceptance
Identification &
participation in
school
11
I am treated with as
much respect as other
students.
Belonging School
belonging Removed Removed
12 I feel very different from
most other students here. Rejection Feeling of
rejection Removed
Identification and
participation in
school
13 I can really be myself at
this school. Belonging School
belonging Acceptance Perception of fitting
in among peers
14 The teachers here respect
me.
Belonging,
Acceptance
School
belonging
Caring
Relationships
Generalized
connection to
teachers
15 People here know that I
can do good work. Belonging School
belonging Removed Removed
16 I wish I were in a
different school. Acceptance Feeling of
rejection Rejection
Identification &
participation in
school
17 I feel proud of belonging Acceptance School Removed Identification &
28
The Simple School Belonging Scale
to (school name). belonging participation in
school
18 Other students here like
me the way I am. Belonging School
belonging Acceptance Perception of fitting
in among peers
29
The Simple School Belonging Scale
Table 2
Phase 1: Exploratory and confirmatory factor loadings, PSSM
EFA Factor Loadings CFA Standardized Loadings
Item 1 2 3 1 2
1 0.836* -0.118* -0.045 0.850
2 0.758* -0.010 -0.196* 0.692
3 0.021 0.750* 0.004 0.762
4 0.783* 0.113* -0.276*
5 0.805* 0.066 0.275*
6 -0.046 0.857* 0.045 0.823
7 0.554* -0.021 0.398*
8 0.756* -0.210* -0.046 0.794
9 0.007 0.574* -0.414*
10 0.647* -0.025 -0.028 0.595
11 0.693* -0.195* 0.032 0.774
12 -0.003 0.755* 0.052 0.502
13 0.663* -0.252* 0.006 0.779
14 0.730* 0.014 0.564*
15 0.722* -0.111* 0.239*
16 -0.245* 0.575* -0.134* 0.815
17 0.762* -0.119* 0.047 0.836
18 0.677* -0.175* -0.009 0.842
*Significant at p<0.05
30
The Simple School Belonging Scale
Table 3
PSSM 3-Factor EFA: Factor Correlations
Factor 1 Factor 2 Factor 3
Factor 1 1.000
Factor 2 -.479 1.000
Factor 3 -.289 .200 1.000
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The Simple School Belonging Scale
Table 4
Phase 2: Exploratory and confirmatory factor loadings, PSSM + New Items
PSSM Questions
EFA Factors Loadings
CFA Standardized
Loadings (Unifactor
Model)
CFA Standardized Loadings
(Multi-factor Model)
1 2 3 4 1 1 2 3
1 I feel like a real part of (school name). 0.769* -0.022 0.039 0.276*
2People here notice when I am good at
something. 0.730* 0.013 0.071 -0.055 0.729 0.727
3It is hard for people like me to be accepted
here. -0.048 0.729* -0.089 0.176*
4Other students in this school take my opinions
seriously. 0.829* 0.112* -0.054 -0.039 0.730 0.719
5Most teachers at this school are interested in
me. 0.386* 0.082* 0.545* 0.044
6 Sometimes I don't feel as if I belong here. -0.195* 0.779* 0.021 0.008 0.959
7There's at least one teacher or adult in this
school that I can talk to if I have a problem. 0.063 -0.011 0.605* 0.109* 0.715
8 People at this school are friendly to me. 0.648* -0.159* 0.198* -0.003 0.748 0.768
9Teachers here are not interested in people like
me. 0.310* 0.555* -0.488* -0.019
10 I am included in lots of activities at this
school. 0.490* 0.02 0.248* 0.035 0.635 0.636
11 I am treated with as much respect as other
students. 0.517* -0.169* 0.314* -0.110*
12 I feel very different from most other students
here. -0.102 0.699* -0.004 0.019 0.508
13 I can really be myself at this school. 0.484* -0.244* 0.258* -0.006
14 The teachers here respect me. 0.045 -0.001 0.832* 0.097* 0.754
15 People here know that I can do good work. 0.279* -0.136* 0.610* -0.091*
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The Simple School Belonging Scale
16 I wish I were in a different school. -0.016 0.603* -0.086* -0.548*
17 I feel proud of belonging to (school name). 0.624* 0.005 0.046 0.503*
18 Other students here like me the way I am. 0.578* -0.160* 0.191* -0.043 0.837 0.802
Additional Belonging Questions
1 I feel loyal to people in (school name). 0.633* 0.121* 0.034 0.380*
2 I feel like I belong to (school name). 0.624* -0.123* -0.043 0.443*
3
I would be willing to work together with
others on something to improve (school
name).
0.336* 0.147* 0.320* 0.384*
4I like to think of myself as similar to others at
(school name). 0.667* -0.085* -0.003 0.170* 0.685 0.679
5Given the opportunity, I would move to a
different school. 0.080* 0.608* 0.007 -0.683*
6 People at (school name) care if I am absent. 0.824* 0.025 -0.09 -0.031 0.739 0.728
7 I fit in with other students at (school name). 0.722* -0.305* -0.042 -0.005
8 I participate in activities at (school name). 0.439* 0.056 0.282* 0.134*
9I would rather attend a different junior high
school. -0.031 0.578* 0.000 -0.666*
10 I feel out of place at (school name). -0.302* 0.685* 0.067* -0.162*
11 I feel like my ideas count at (school name). 0.671* 0.024 0.181* 0.042 0.791 0.800
12 (School name) is a comfortable place for me. 0.726* -0.053* 0.003 0.331*
13 I feel like I matter to people at (school name). 0.857* -0.049* 0.008 0.071* 0.890 0.885
14 People really listen to me when I am at school. 0.814* -0.003 0.098* -0.097* 0.837 0.838
*Significant at p<0.05
33
The Simple School Belonging Scale 34
The Simple School Belonging Scale
Table 5
PSSM + New Items 4-Factor EFA: Factor Correlations
Factor 1 Factor 2 Factor 3 Factor 4
Factor 1 1.000
Factor 2 -.399 1.000
Factor 3 .623 -.183 1.000
Factor 4 .240 -.126 .306 1.000
35
The Simple School Belonging Scale
Table 6
Phase 3: Item parameter estimates from graded response model: SSBS
Item Source Threshold 1 Threshold 2 Threshold 3 Discrimination
People here notice when I am good at something. PSSM 2 -1.91 -0.71 0.85 2.10
Other students in this school take my opinions
seriously. PSSM 4 -1.81 -0.34 1.62 2.09
People at this school are friendly to me. PSSM 8 -2.13 -1.22 0.78 2.36
I am included in lots of activities at this school. PSSM 10 -1.99 -0.32 1.48 1.47
Other students here like me the way I am. PSSM 18 -2.20 -1.32 0.50 2.25
I like to think of myself as similar to others at (school
name). New 4 -1.58 -0.47 1.19 1.86
People at (school name) care if I am absent. New 6 -1.72 -0.59 0.95 2.10
I feel like my ideas count at (school name). New 11 -1.53 -0.29 1.29 2.49
I feel like I matter to people at (school name). New 13 -1.55 -0.68 0.77 3.86
People really listen to me when I am at school. New 14 -1.47 -0.43 0.99 3.25
36
The Simple School Belonging Scale
Figure 1. Sample category response curve for item 4, suggesting good category functioning and
good discrimination. Curves for other items on the scale are similar.
37
The Simple School Belonging Scale
Figure 2. Item information curves for final unidimensional scale showing peak information is
available between -2 and 2.
38
