(p.190) Appendix 2 Details of the Structural Equation Analyses
(p.190) Appendix 2 Details of the Structural Equation Analyses
The reported analyses were performed using variance-covariance matrices with pairwise deletion of missing values. Two alternative methods of dealing with missing values were used: listwise deletion and estimation using expectation-maximization method. All three methods yielded very similar results.
In the analyses, three indicators per latent construct were used, unless a construct was indicated by a single item. In the latter cases, the measurement error of a single indicator was provided to the program, assuming reliability of 0.80. In cases of multiple indicators, using the accepted approach of parceling (Bandalos, 2002; Stacy, Bentler, & Flay, 1994), each latent variable was indicated by one third of the items that make up the scale. Item parcels were constructed so that their kurtosis statistic would be minimized. To achieve this, items with largest kurtosis were combined with items with smallest kurtosis, and so on. In spite of these, many of the observed variables were nonnormally distributed due to the nature of the phenomena under investigation (victimization). To overcome this violation of SEM assumptions, we employed a maximum-likelihood estimation method with robust standard errors (Hu & Bentler, 1999) together with the Satorra-Bentler rescaled chi-square statistic (Satorra & Bentler, 1994, 1999). This statistic compensates for multivariate nonnormality of variables. Difference between two scaled chi-squares doesn’t distribute as chi-square. Therefore, in computing significance of differences between models, we used the Satorra-Bentler scaled difference test (Satorra & Bentler, 1999).
Following recommendations of Hu and Bentler (1999), we report fit indexes of two types: Non-Normed Fit Index (NNFI, also known as TLI) and Comparative Fit Index (CFI), and two indexes of misfit: Root Mean-Square Error of Approximation (RMSEA) and Standardized Root Mean-Square Residual (SRMR). NNFI (p.191) and CFI close to or above 0.95 combined with RMSEA below 0.07 and SRMSR below 0.09 are considered indicative of acceptable fit.
The model presented in this chapter tested two types of hypotheses: direct effects of independent on dependent variables and mediated effects. Following Kenny, Kashy, and Bolger (1998, p. 10), we considered two pieces of evidence as compatible with a mediation hypothesis: (1) a significant correlation between an independent variable and a mediator, and (2) a significant indirect effect of the independent on the dependent variable.
Following the test of a model for the whole sample, we proceeded to testing differences between subgroups, such as male students versus female. The multigroup analysis is done in several steps. First, all factor loadings, paths, and covariances are constrained to be equal in two groups, and we tested the hypothesis that the same model is valid for both groups. Second, selected constraints on paths are released one at a time to test whether the model fit could be improved by postulating differences in paths between groups. The constraints to release were selected by inspection of paths in a multigroup model where they were unconstrained. Those paths were selected for testing for which standardized coefficients were different by at least 0.10 in two groups. It should be noted that in SEM, difference between paths in two groups is tested using unstandardized coefficients. A difference of 0.10 in standardized values could be insignificant, while a much smaller difference could be significant. We preferred this approach to ensure that only meaningful differences were chosen as candidates for analysis. After each of the differences were tested one by one, we tested a model in which all paths with significant differences between groups were left unconstrained for equality and assessed improvement in fit over the fully constrained model.
JUNIOR HIGH AND HIGH SCHOOLS
The initial sample consisted of 10,400 respondents (Rs). They came from 162 different schools, 405 classes. Those respondents who had more than five missing values on 26 observed variables used in the analysis (see below) were deleted from the database. The resulting file had 10,150 respondents. All analyses were performed on data with pairwise deletion of missing data.
Four dummy variables were constructed:
1. School type, distinguishing between junior high (marked 1) and high school students.
2. Religious-nonreligious, comparing between religious Jewish (1) and other students.
3. Culture/ethnicity: Arab schools’ students received value 1 on this variable.
4. Gender (with value 1 assigned to boys).
RISKY PEER GROUP BEHAVIOR
Using a scale with 14 items measured on a 1–5 scale (5 meaning high level of risk), a factor analysis performed on these items showed that the first factor was responsible for most of the variance (Eigenvalue of 6.10) and the next ones were much weaker (Eigenvalues 1.31, 1.11). In principal components, all items were heavily loaded on the first factor. Consequently, we treated the items as constituting one scale. Preliminary tests of the measurement model showed that the two items with the smallest distribution (3 and 4) reduced the internal consistency of the measurement; they were deleted from the analysis. The alpha of the overall risk scale was 0.89.
- RIS1 Students get into fights.
- RIS2 Students drink alcoholic drinks (like wine, beer).
- RIS5 Students bring other weapons to school (such as knives, clubs).
- RIS6 Students destroy things in schools, put graffiti on walls, damage furniture.
- RIS7 Students steal things from other students or teachers.
- RIS8 Students threaten or bully other students.
- RIS9 There is dangerous gang activity in my school.
- RIS10 The boys sexually harass the girls (make obscene suggestions, touch, peep).
- RIS11 Outsiders (adults) enter the campus during the school day and threaten, harass, or get into fights with students or teachers.
- RIS12 Teachers or other staff members curse, insult, or verbally humiliate students.
- RIS13 Teachers or other staff members hurt students (slap, pinch, push).
- RIS14 Teachers or other staff members “come on to” the girls, sexually harass, or bother them.
Using a scale with 21 items with 1–4 response scale (4 meaning positive climate), factor analysis showed that all of these items could be best explained by one factor (Eigenvalue 9.20, with the next factors of 1.29 and 1.08 only). Nevertheless, we decided to use our theory-based categorization of the items and constructed three indicators. Three negatively worded items (10, 14 and 15) were unrelated to the others in item analysis and they were deleted. The overall alpha of the remaining 18 items was 0.94. Three indicators were formed in the following way:
(p.193) I. Policy
- CLIM1 When students break the rules, they are treated firmly but fairly.
- CLIM2 My teachers are fair.
- CLIM3 It pays to obey the rules at my school.
- CLIM4 The rules at my school are fair.
- CLIM5 Teachers do a good job of protecting students from troublemakers.
- CLIM6 When I complain about somebody hurting me the teachers help me.
- CLIM7 In my school there are clear and known rules against violence.
- CLIM8 In my school there are clear and known rules against sexual harassment.
- CLIM9 When boys sexually harass girls, the teachers interfere in order to stop it.
- CLIM11 In my school, students participate in making important decisions and in making the rules.
- CLIM12 In my school students play a significant role in taking care of violence problems.
- CLIM13 Staff in my school make efforts to involve students in important decisions.
III. Teacher support
- CLIM16 When students have an emergency (or a serious problem), an adult is always there to help.
- CLIM17 My teachers respect me.
- CLIM18 I can trust most adults in this school.
- CLIM19 I have close and good relationships with my teachers.
- CLIM20 Teachers in this school care for the students.
- CLIM21 I am comfortable talking to teachers when I have a problem.
STAFF RESPONSE TO VIOLENCE
Staff response was measured with a single item: Overall, in your opinion, how are the principal and teaching staff dealing with violence when it occurs in your school? This item was measured on a 1–4 scale. It was reverse-coded so that 4 meant effective coping.
VICTIMIZATION BY STAFF
This scale consisted of eight yes-no items:
- STF1 Seized and shoved you on purpose.
- STF2 Kicked or punched you.(p.194)
- STF3 Pinched or slapped you.
- STF4 Mocked, insulted, or humiliated you.
- STF5 Made sexual comments to you.
- STF6 Tried to come on to you (sexually).
- STF7 Cursed you.
- STF8 Touched or tried to touch you sexually.
The items were recoded as 1 (yes) and 0 (no). In cases where a respondent referred to at least one item in the scale, meaning that he or she read the item and responded, the missing values in the rest of the items were turned to 0 (assuming that a blank means no). The alpha of the entire scale was 0.80.
This subscale of the victimization scale consisted of all of the nine items that were identified as mild/moderate aggressive behaviors in the exploratory factor analysis:
- RAGR2 A student used a rock or another instrument in order to hurt you.
- RAGR9 A student threatened to harm or hit you.
- RAGR11 You were involved in a fistfight.
- RAGR12 You were kicked or punched by a student who wanted to hurt you.
- RAGR15 A student seized and shoved you on purpose.
- RAGR18 A student tried to intimidate you by the way he or she was looking at you.
- RAGR19 A student cursed you.
- RAGR20 A student mocked, insulted, or humiliated you.
- RAGR23 A student stole your personal belongings or equipment.
These items were recoded as 1 (at least once) and 0 (no). In cases where there were missing values in some, but not other, items in the scale, they were converted to 0. The alpha of the total scale was 0.82.
This subscale of the victimization scale consisted of nine items identified as severe behaviors in the exploratory factor analysis:
- RAGR1 A student cut you with a knife or a sharp instrument on purpose.
- RAGR3 You were blackmailed under threats by another student (for money, valuables, or food).(p.195)
- RAGR7 A student threatened you with a gun and you saw the gun.
- RAGR8 A student threatened you with a knife and you saw the knife.
- RAGR10 Gang members at school threatened, harassed, and pressured you.
- RAGR13 A student gave you a serious beating.
- RAGR14 You were involved in a fight, were hurt, and required medical attention.
- RAGR17 You saw a student in school with a gun.
- RAGR24 Students threatened you on your way to or from school.
These items were recoded as 1 (at least once) and 0 (no). In cases in which there were missing values in some, but not other, items in this scale, they were converted to 0. In a preliminary analysis of the measurement, item 8 was found to reduce the internal consistency and was removed. The alpha of the total scale with the remaining eight items was 0.83.
These behaviors were assessed with seven yes-no items, recoded as 1 (at least once) or 0 (no):
- SEX1 A student tried to kiss you without your consent.
- SEX2 Sexually insulting things about you were written on walls or sexual rumors were spread about you.
- SEX3 A student peeped while you were in the bathroom or the locker room.
- SEX4 A student touched or tried to touch you or to pinch you in a sexual way without your approval.
- SEX5 A student tried to come on to you (sexually) and made sexual comments that you did not want.
- SEX6 A student took or tried to take your clothes off (for sexual reasons).
- SEX7 A student showed you obscene pictures or sent you obscene letters.
Missing values were treated as described above. Alpha was 0.80.
SEVERITY OF THE VIOLENCE PROBLEM
Severity of student victimization at school was measured with a single item: What is the magnitude of the school violence problem in your school? The 1–5 response scale was coded so that high values meant high severity.
(p.196) NONATTENDANCE DUE TO FEAR
This subject was measured with a single item: Have you stayed at home because you were afraid that someone may hurt you? The scale was 0 = no, 1 = once, 2 = twice, 3 = more.
Sample and Measures
The initial sample consisted of 6,013 respondents. They came from 77 different schools, with three grades (4 through 6) sampled in each school.
Those respondents who had more than three missing values on 22 observed variables used in the analysis were deleted from the database. The resulting file had 5,675 respondents. All analyses were performed on data with pairwise deletion of missing data.
The indicators were constructed in ways similar to the ones described for the secondary schools.