The building blocks of model 7: autoregressive models 1-

Chapter 4 Models and measurement methodology Introduction

4.2 The building blocks of model 7: autoregressive models 1-

Models 1-6 developed for this analysis are described in Table 4.1. The table presents the latent factor names and the LSYPE manifest variables that were used as indicators in each model. Models 1-6 are presented in their generic form, with invariance constraints imposed on their measurement model before actual estimation. When the models were actually fitted to each minority sample, their error structure was modified to achieve optimal fit. The estimated models with their final error structures are fully described and discussed in chapters 6 and 7. All models were developed in a 4- step procedure, following the recommendations of Mulaik and Millsap (2000). This procedure involved selection of the original optimal set of indicators for all occasions by means of exploratory factor analysis (EFA) (step 1); specifying a congeneric CFA model with simplex factor structure per occasion, if such specification was supported by the data (step 2); specifying the complete

autoregressive CFA model and testing for goodness of fit (step 3) and respecifying the

Table 4.1: Operationalization of models 1-7 Name, role in the final model

(Exogenous or predictor (P), endogenous or Outcome (O); endogenous or Mediator (Me) and number of occasions in local model (2 or 3)

LSYPE wave- specific Indicators and derived scales used in models 1-7

Actual wording of LSYPE variables that were used as indicators or in scale construction(parcels) Type of variable Type and level of longitudinal factorial invariance achieved

Model 1 FAMCIRC1

FAMCIRC2 ( parental social position

and associated level of family material circumstances, measured at

two occasions based on LSYPE wave1 and wave2 repeated measures); Role in final model (7): exogenous

r_W1nsseccatdad

r_W2nsseccatdad Derived variable: father’s socioeconomic classification (‘What is/was your (main) job?; What do/did you mainly do in your job?; What training or qualifications are/were needed for that job?; Did you have formal responsibility for supervising the work of other employees?’, LSYPE waves 1-2

Ordered-categorical [8 categories representing a shortened version of the 17 category NS-SEC (8=higher managerial, 1=never worked/ long-term unemployed)]

Configural (equal form across occasions)

Full metric (equal loadings) Full scalar (equal intercepts)

r_W1nsseccatmum

r_W2nsseccatmum Derived variable: mother’s socioeconomic classification, (‘What is/was your (main) job?; What do/did you mainly do in your job?; What training or qualifications are/were needed for that job?; Did you have formal responsibility for supervising the work of other employees?’ LSYPE waves 1-2

Ordered-categorical [8 categories representing a shortened version of the 17 category NS-SEC (8=higher managerial, 1=never worked/ long-term unemployed)] W1GrssyrHHbands

W2GrssyrHHbands LSYPE-derived variables based on W1 and W2 all-source gross family income, respectively (‘What is your basic hourly rate?; and what time period did this cover?; and what your TAKE-HOME pay, that is, AFTER all deductions?’.

Ordered-categorical (8 categories of gross family income ranging from 1 (lowest to 8 (highest)

HHdepW1

HHdepW2 Wave1 and wave2 unweighted summative scales including 3 items per wave (drawn from LSYPE wave1 and 2 variables): (a) r_W1condur4MP

(r_W2condur4MP) (‘Does your household have any of the following items: a telephone’ at wave1 (wave2) with 4 categories, 4=Yes, both mobile and landline; 3=Yes, fixed telephone only;

2=Yes, mobile only; 1=No (neither mobile nor fixed) (b) r_W1condur5MP,

(r_W2condur5MP) a binary categorical variable (‘Does your household have any of the following items in your (part of) accommodation?: a home computer’ with 2=Yes, 1=No)

(r_W1condur6MP) a binary categorical variable (‘Can you, or other members of your household, get access to the internet either just for email or to browse the Web, from home?’) with 2=Yes and 1=No. Cronbach’s α, wave1 =0.57 (3 items)

Cronbach’s α, wave2 =0.58 (3 items)

Ordered-categorical variable (parcel) with values 3=lowest; 8=highest

Model 2 PAR1 PAR2 PAR3

Representing potential ‘home- related’ mediator 2 (Me1), operationalising a measure of ‘parent - child conflict’ based on LSYPE wave1, 2 and 3 repeated measures. Role in final model (7): endogenous

W1parqualMP W2parqualMP W3parqualMP

Parent-reported frequency of arguing with the young person (‘Young people often have arguments with their parents about things like young person’s friends, their clothes or hairstyle, things they do when they go out or what time they come back. How often would you say you argue with the YP?)

Ordered-categorical variable with four categories originally coded as 4=never and 1=most days. The original coding was retained so that a high value denoted good parent-child relationship.

Configural (equal form across occasions)

Full metric (equal loadings) Full scalar (equal intercepts)

r_W1kiddifMP r_W2kiddifMP r_W3kiddifMP

Parent-reported assessment of quality of relationship with the young person (‘All in all, how well or how

badly would you say you get on with YP?) Ordered-categorical variable with four categories, reverse- coded so that a high value denoted good parent-child relationship with 4=very well and 1=very badly.

Model 3 HW1 HW2

Representing potential ‘home- related’ mediator (Me2),

operationalising a measure of pupils’ ‘engagement with homework’ based on LSYPE wave1 and 2 repeated measures. Role in final model (7): endogenous

W1hwndayYP

W2hwnday1YP W1hwndayYP: ‘During an average week in term time, on How many evenings do you do any homework? (Please just think about Monday to Friday evenings during term time)’ and W2hwnday1YP: ‘During term time, how many evenings a week do you do any homework?’

Interval-level variables with 5=five evenings per week and 0=does not do any HW/not assigned homework.

Configural,

Partial metric (2/3 loadings invariant)

Partial scalar (2/3 intercepts invariant)

W1hwdoYP

W2hwdoYP Young person-reported frequency of homework set in term time: ‘How often are you given HW?’ asked at LSYPE wave 1 and 2 Ordered-categorical variables with five categories, reverse- coded so that 5=most days and 1=never assigned any homework

Model 4 SCH1 SCH2 SCH3

Representing potential ‘school- related’ mediator 1 (Me3), operationalising a measure of ‘young people’s feelings about their school’ based on LSYPE wave1, 2 and 3 repeated measures. Role in final model (7): endogenous

r_W1yys1YP r_W2yys1YP r_W3yys1YP

Young person-reported agreement with statement: ‘Below are some things young people have said about how they feel about school. For each statement below, please say whether or not you agree with it. Please give an answer for each of them: How much do you agree or disagree that: I’m happy when I am at school’ asked at LSYPE wave1-3

Ordered-categorical variable with four categories reverse coded so that a high value denoted strong positive feeling about school with 4=strongly agree and 1=strongly disagree

Configural (equal form across occasions)

Full metric (equal loadings) Full scalar (equal intercepts)

W1yys4YP W2yys4YP W3yys4YP

Young person-reported agreement with statement: ‘Most of the time I do not want to go to school’ asked at

LSYPE wave1-3. Ordered-categorical variable with four categories originally

coded as 4=strongly disagree and 1=strongly agree. The original coding was retained so that a high value denoted strong positive feeling about school.

r_W1yys6YP r_W2yys6YP r_W3yys6YP

Young person-reported agreement with statement: ‘On the whole, I like being at school’ asked at LSYPE

wave1-3. Ordered-categorical variable with four categories reverse

coded so that a high value denoted strong positive feeling about school with 4=strongly agree and 1=strongly disagree W1yys9YP

W2yys9YP W3yys9YP

Young person-reported agreement with statement,: ‘I’m bored at lessons’ asked at LSYPE wave1-3. Ordered-categorical variable with four categories originally coded as 4=strongly disagree and 1=strongly agree. The original coding was retained so that a high value denoted strong positive feeling about school.

Model 5 TCH1 TCH2

Representing potential ‘school- related’ mediator 2 (Me4), operationalising a measure of ‘young people’s assessments about their teachers’ disciplinary effectiveness based on LSYPE wave 1 and 2 repeated measures. Role in final model (7): endogenous

r_W1yys15YP

r_W2yys15YP Young person-reported assessment of the proportion of their teachers who are effective in keeping order and discipline (‘Now please answer the next few questions by typing the number which is closest to what you think is true…To how many of your teachers does the following statement apply: The teachers in my school make it clear how we should behave’) asked at LSYPE wave1-2.

Ordered-categorical variable with five categories reverse coded so that a high value denoted higher proportions of young person’s teachers at school with 5=all of my teachers and 1=none of my teachers

Configural (equal form across occasions)

Full metric (equal loadings) Full scalar (equal intercepts)

r_W1yys16YP

r_W2yys16YP Young person-reported assessment of the proportion of their teachers who are effective in keeping order and discipline (‘How many teachers this applies to: The teachers in my school take action when see anyone breaking school rules’) asked at LSYPE wave1-2.

r_W1yys18YP

r_W2yys18YP Young person-reported assessment of the proportion of their teachers who are liked by pupil (‘How many teachers this applies to: I like my teachers’) asked at LSYPE wave1-2. Ordered-categorical variable with five categories reverse coded so that a high value denoted higher proportions of young person’s teachers at school with 5=all of my teachers and 1=none of my teachers

r_W1yys19YP

r_W2yys19YP Young person-reported assessment of the proportion of their teachers who are effective in keeping order and discipline (‘How many teachers this applies to: My teachers can keep order in class’) asked at LSYPE wave1-2.

Model 6 YPEX1 YPEX2 YPEX3

(Outcome, representing young

people’s educational expectations regarding continuing in full-time education (FTE) after year 11 or age 16, measured at three occasions,

based on LSYPE wave1-3 repeated measures. Role in final model (7): endogenous

r_W1heposs9YP r_W2heposs9YP r_W3heposs9YP

Young people’s self-reported likelihood to continue in FTE after year 11 (‘How likely do you think is it that

you will ever apply to go to university to do a degree?’ asked at LSYPE waves1-3) r_W1heposs9YP Ordered-categorical with four categories reverse coded so that 4=very likely, 1=not at all likely.

Configural (equal form across occasions)

Full metric (equal loadings) Full scalar (equal intercepts) r_W1hlikeYP

r_W2hlikeYP r_W3hlikeYP

Young people’s self-reported likelihood of being accepted at t he university, if applied (‘How likely do you

think it is that if you apply to go to university you will get in?’ asked at LSYPE waves1-3) Ordered-categorical with four categories reverse coded so that 4=very likely, 1=not at all likely.

models for models 1-6 described below which could then be tested for longitudinal and cross-group measurement and structural invariance. These invariance tests are reported in chapter 6.

I necessarily included the names and actual wording of the LSYPE variables involved in each model in this chapter. This might seem a little unorthodox since the data source will be formally presented in chapter 5. However, this transgression was done for two important reasons. The first served the interest of describing models 1-6 as completely as possible. The second was to help the reader identify which variable goes to which model so that their interconnection as integral parts of model 7 can be unambiguous. I therefore believe that this presentation will give a more rounded picture of each model than if the models were presented in a more abstract form leaving the reader to match variables to models after the fuller LSYPE data description in chapter 5. Also, in choosing this order of presentation, I have followed the order of presentation in quantitative journals where the model specification typically precedes description of the sample and data source. Having an unambiguous picture of each model, the reader can then focus on the cross-group comparisons of their observed indicators when the LSYPE data are presented in chapter 5.

Model 1: Parental social position and family material circumstances (level of deprivation) (FAMCIRC, truncated to FAM in certain Tables in chapter 7)

Model 1 (parental social position, FAMCIRC) examines change in parental social position including family material circumstances between pupils’ ages 14 to 15. FAMCIRC is the exogenous predictor in the final multiple mediator model (model 7). Table 4.1 above describes the LSYPE variables at wave 1 and 2 that were used as indicators of FAMCIRC1 (occasion 1, age 14) and FAMCIRC2 (occasion 2, age 15). Figure 4.3 illustrates Model 1.

FAMCIRC is defined by father’s and mother’s NS-SEC status, gross family income for waves 1 (age 14) and 2 (age 15) and a measure of family-level material circumstances (deprivation) at LSYPE wave 1 and 2 which is described below. Father’s and mother’s NS-SEC status

corresponding to wave 1 (age 14) and 2 (age 15) were recoded to arrive at an 8-level father’s and mother’s socioeconomic classification schema. This classification followed the subcodes and rank order suggested by the original LSYPE coding of father’s and mother’s NS-SEC consisting of 17 codes for occupations4. The variables for gross family income retained their original LSYPE coding

4_{Collapsing the original occupational codes derives 3 NS-SEC schemas (ONS, 2010). The 8-point schema used in this} thesis aggregates ‘broad social class groupings' (Dex, Ward and Lindley, 2007, p. 6); the 5-point and a 3-point schemas

and ranged from 1= < £5000 to 8 = >£ 50000 per annum (see Table 4.1 or Figure 4.3 for variable labels).

Figure 4.3: The autoregressive model for FAMCIRC (Model 1) with metric and scalar invariance constraints in place.

Legend: Y1, Y5 = r_W1nsseccatdad, r_W2nsseccatdad (father’s NS-SEC, LSYPE waves 1-2), Y2, Y6 =

r_W1nssecmum, r_W2nssecmum (mother’s NS-SEC, LSYPE wave 1-2), Y3, Y7 = HHdepW1, HHdepW2 (family level deprivation (material circumstances) score, LSYPE waves 1-2), Y4, Y8 = W1GrssyrHHbands, W2GrssyrHHbands (gross family income, LSYPE waves 1-2)

The measure for family level material circumstances (deprivation) was an unweighted summative scale derived from the following three LSYPE wave 1 and wave 2 variables: (a) ‘Does your household have any of the following items: a telephone’, a categorical variable with 4 categories, 4=Yes, both mobile and landline; 3=Yes, fixed telephone only; 2=Yes, mobile only; 1=No (neither mobile nor fixed). (b) ‘Does your household have any of the following items in your (part of) accommodation?’: ‘a home computer’, a binary categorical variable with two categories (2=Yes, 1=No). (c) ‘Can you, or other members of your household, get access to the internet either just for email or to browse the Web, from home?’, a binary categorical variable with two categories (2=Yes and 1=No).

were no significant differences in either the loadings of the FAMCIRC construct or the structural estimates of the multigroup solution of model 7. This suggests that the models were robust to the three different versions of the NS-SEC

The order of the four categories of the variables (a) and (b) above was confirmed by regressing the W2 Index of Multiple Deprivation (LSYPE wave 2 IMD score) on the categories of the variables by means of two logistic regressions. The z-score distribution of the LSYPE wave 2 Index of Multiple Deprivation (IMD) coded as 1 (including all the IMD scores above the mean ranging from 0.00 to +3.00SD) and 0 (including all the IMD scores below the mean, ranging from -3.00SD to 0.00 = 0) was the dependent variable in both regressions. The derived odd ratios were contrasted to the reference category (highest, coded ‘4’ in the original variable = having both fixed and mobile phones). The analysis indicated a ranking of the differential propensity of each category of the above variables at age 14 to be associated with above the average IMD scores at age 15. Unsurprisingly, the category coded 1 (lowest) was more likely to be associated with below the average IMD scores, while the category coded 3 was more likely to be associated with above the average IMD scores as compared to the reference category (category 4). Categories 1-4 of the variables could therefore be construed as reflecting an underlying dimension of family-level material circumstances (deprivation), with 1 signifying the worst material circumstances (highest deprivation) and 4 the best (lowest deprivation).

With the three items combined, the additive scales HHdepW1 (wave 1, age 14) and HHdepW2 (wave 2, age 15) ranged from 3=lowest to 8=highest. The reliability of the scale with only 3 items, was acceptable at wave 1 (Cronbach’s α = 0.607 for HHdepW1) and marginally acceptable at wave 2 (Cronbach’s α = 0.589 for HHdepW2). All the indicators of FAMCIRC were treated as continuous based on simulation studies that suggested that an ordinal variable can be treated as continuous provided it had ≥ 5 categories (Babakus, Ferguson and Jöreskog, 1987; Bentler and Chou, 1987; Byrne, 2010). Full description of the variables entering the two occasions of the FAMCIRC model per each minority group will be shown in chapter 5.

Model 2: Parental-child conflict (PAR)

Model 2 (parent-child conflict, PAR) estimates change in parental-child conflict between pupils’ ages 14 to 16. PAR is a potential mediator in the final mediator model (model 7). The LSYPE wave 1, 2 and 3 variables used as indicators of PAR1 (age 14), PAR2 (age 15) and PAR3 (age 16) are discussed below. Figure 4.4 presents Model 2.

(see Table 4.1 or Figure 4.4 for variable labels). Both variables are ordered-categorical with four categories originally coded as 4=never and 1=most days as a Likert scale. The original coding was retained so that a high value denoted low-parent child conflict. The variables were treated as continuous. Full description of these variables can be found in chapter 5.

Figure 4.4: The autoregressive model for PAR (Model 2) with metric, scalar and theta invariance constraints in place.

Legend: Y1, Y3, Y5 = r_W1parqualMP, W2parqualMP and W3parqualMP (mother’s frequency of arguing with young

person, LSYPE waves 1-3), Y2, Y4, Y6 = r_W1kiddifMP, r_W2kiddifMP and r_W3kiddifMP (mothers’ assessment of how bad relationship is with young person, LSYPE waves 1-3).

Model 3 Pupils’ engagement with homework (HW)

Model 3 (pupils’ engagement with homework, HW) examines change in young people’s

engagement with homework between ages 14 to 15. The LSYPE did not include these measures at wave 3. Along with parent-child conflict (PAR), engagement with homework is a potential mediator representing influences of the home context. Figure 4.5 shows Model 3 (HW).

Model 3 captures two dimensions of homework available in the LSYPE: (a) time spent on

homework (in number of weekday evenings spent on homework) by the pupil during a typical term time week at ages 14 and 15, an interval-level variable; (b) amount of homework set, expressed by the pupil as the frequency homework was assigned during term time, ranging from 1 = ‘never assigned homework’ to 5 = ‘most days’, at ages 14 and 15, an ordered-categorical variable (see

Table 4.1 or Figure 4.5 for variable labels). Because the autoregressive model for HW has only two occasions and two indicators per occasion, further constraints had to be imposed to identify the measurement model with positive degrees of freedom (i.e., to decrease t, equation 4.11). The

Figure 4.5: The autoregressive model for HW (Model 3) with metric and scalar invariance constraints in place.

Legend: Y1, Y3 = W1hwndayYP, W2hwnday1YP (pupil-reported number of evenings spent on homework, LSYPE

waves 1-2), Y2, Y4 = W1hwdoYP, W2hwdoYP (pupil-reported frequency homework was assigned during term week, LSYPE waves 1-2).

invariance constraints imposed on the indicator loadings and intercepts produced extra degrees of freedom and the model was identified (Arbuckle, 2009). These constraints are illustrated in Figure 4.5. However, because indicator errors were freely estimated, the measurement model allowed the free estimation of only a single error covariance.

Model 4 Pupils’ feelings about school (school affect, SCH)

Model 4 (pupils’ feelings about school, SCH) operationalised pupils’ feelings about their school. SCH is a potential mediator in the final model. Figure 4.6 shows model 4. Based on the result of prior EFA, the model used four LSYPE items out of possible 14 that loaded consistently the highest on the latent construct SCH at ages 14, 15 and 16. The items reported pupils’ agreement with the following statements : (a) ‘I’m happy when I am at school’ (b) ‘Most of the time I do not want to go to school’; (c) ‘On the whole, I like being at school’; (d) ‘I’m bored at lessons’ (see Table 4.1 for

In document An exploration of ethnic differences of the influences of home and school on the development of young people’s educational expectations for university study between ages 14 to 16 (Page 75-87)