School Adjustment, Motivation, and Academic Functioning

Project brief for the SEM course dataset

1 Project brief

A colleague asks you to help analyse data from a multi-school study of secondary-school students. The broad aim is to understand how school context, motivation, school adjustment, emotional functioning, and academic achievement are related.

The substantive focus is not a single variable. The dataset is meant to support several linked questions about academic functioning:

  • Why do some adolescents report stronger academic self-efficacy than others?
  • How are teacher support and school belonging related to school anxiety?
  • Are school anxiety and academic self-efficacy associated with academic achievement?
  • Do these associations remain visible over time?
  • Are individuals with incomplete follow-up data different from those with more complete data?

The dataset is simulated, but it is intentionally not clean. You should expect realistic complications: skewed ordinal indicators, binary test items, noisy task indicators, missing data, group differences, and clustered observations.

The goal is not to find the one correct model. The goal is to make defensible analytic choices, explain them clearly, and connect the statistical results back to the substantive questions.

What you are expected to decide

You need to decide how to represent the constructs, how to handle missing data, whether clustering matters, and which analytic strategy is appropriate for each question. You may begin with descriptive statistics, sum scores, correlations, regressions, and path models before moving to latent variable models.

2 Dataset structure

Each row corresponds to one student. Students are nested in classes, and classes are nested in schools.

Code 
sample_structure <- dat |>
  summarise(
    n_students = n(),
    n_schools = n_distinct(school_id),
    n_classes = n_distinct(class_id),
    mean_class_size = mean(class_size, na.rm = TRUE),
    min_class_size = min(class_size, na.rm = TRUE),
    max_class_size = max(class_size, na.rm = TRUE)
  )

kable(sample_structure, digits = 2)
n_students n_schools n_classes mean_class_size min_class_size max_class_size
2394 30 120 20.55 12 30

The main contextual and clustering variables are:

Variable Description
school_id School identifier
class_id Class identifier nested within school
region Macro-region of the school
school_type General, technical, or vocational school
school_resources Standardized school-level resource index
class_climate_mean Standardized class-level climate index

3 Main variables and measures

This section describes the main variables used in the project. The dataset contains more variables than those listed here, but these are sufficient for the main research questions.

3.1 Background variables

Variable Description
age Student age
grade School grade
gender Student gender
ses Standardized socioeconomic status
parent_edu Highest parental education, ordinal 1-5
books_home Approximate books at home, ordinal 1-5
language_home Majority language or other home language
migration_background Migration background indicator
special_education_support Formal learning-support indicator

These variables can be treated as predictors, covariates, grouping variables, or auxiliary variables, depending on the research question.

3.2 Observed academic and behavioural variables

Variable Description
gpa_t1, gpa_t2, gpa_t3 Grade point average across three waves
math_grade_t1 Baseline math grade
language_grade_t1 Baseline language grade
absences_t1, absences_t2, absences_t3 Number of school absences
study_hours Weekly study hours
screen_time Daily recreational screen time in hours
homework_completion Homework completion frequency, ordinal 1-5
teacher_rating_effort Teacher-rated student effort

3.3 Academic self-efficacy

Academic self-efficacy refers to perceived competence in understanding, learning, and succeeding in school tasks.

It is measured at three waves using five ordinal indicators per wave:

se1_t1-se5_t1
se1_t2-se5_t2
se1_t3-se5_t3

3.4 School anxiety

School anxiety refers to worry, tension, and avoidance related to school tasks, classroom participation, and evaluation.

It is measured at three waves using six ordinal indicators per wave:

anx1_t1-anx6_t1
anx1_t2-anx6_t2
anx1_t3-anx6_t3

3.5 School belonging

School belonging refers to perceived acceptance, safety, and connectedness at school.

It is measured at three waves using five ordinal indicators per wave:

bel1_t1-bel5_t1
bel1_t2-bel5_t2
bel1_t3-bel5_t3

3.6 Mastery goal orientation

Mastery goal orientation refers to valuing learning, improvement, and mastery.

It is measured at baseline using five ordinal indicators:

mast1_t1-mast5_t1

3.7 Perceived teacher support

Perceived teacher support refers to students’ perceptions that teachers explain clearly, notice difficulties, treat students fairly, encourage effort, and provide useful feedback.

It is measured at baseline using five ordinal indicators:

ts1_t1-ts5_t1

3.8 Academic reasoning ability

Academic reasoning ability is measured at baseline using 12 correct/incorrect indicators:

abil1-abil12

The items vary in difficulty. The variables are binary: 0 indicates an incorrect response and 1 indicates a correct response.

3.9 Attention regulation

Attention regulation is measured at baseline using four continuous task indicators:

att_acc
att_rt_inv
att_inhibit
att_switch

Higher values indicate better attention regulation or better task performance.

4 Descriptive overview

Use the descriptive statistics as the starting point for analysis. Before testing any hypothesis, inspect distributions, missingness, and the basic structure of the sample.

4.1 Demographics

Code 
demo_continuous <- dat |>
  summarise(
    mean_age = mean(age, na.rm = TRUE),
    sd_age = sd(age, na.rm = TRUE),
    mean_ses = mean(ses, na.rm = TRUE),
    sd_ses = sd(ses, na.rm = TRUE)
  )

kable(demo_continuous, digits = 2)
mean_age sd_age mean_ses sd_ses
15.9 1.11 0 1
Code 
dat |>
  count(gender, name = "n") |>
  mutate(percent = 100 * n / sum(n)) |>
  arrange(desc(n)) |>
  kable(digits = 1)
gender n percent
girl 1220 51.0
boy 1124 47.0
another_or_no_answer 50 2.1
Code 
dat |>
  count(school_type, name = "n") |>
  mutate(percent = 100 * n / sum(n)) |>
  arrange(desc(n)) |>
  kable(digits = 1)
school_type n percent
general 896 37.4
vocational 770 32.2
technical 728 30.4

4.2 Main observed outcomes

Code 
observed_vars <- c(
  "gpa_t1", "gpa_t2", "gpa_t3",
  "absences_t1", "absences_t2", "absences_t3",
  "study_hours", "screen_time", "teacher_rating_effort"
)

observed_desc <- dat |>
  summarise(
    across(
      all_of(observed_vars),
      list(
        mean = ~ mean(.x, na.rm = TRUE),
        sd = ~ sd(.x, na.rm = TRUE),
        missing = ~ mean(is.na(.x))
      )
    )
  ) |>
  pivot_longer(
    everything(),
    names_to = c("variable", ".value"),
    names_pattern = "(.*)_(mean|sd|missing)$"
  )

kable(observed_desc, digits = 2)
variable mean sd missing
gpa_t1 7.00 0.90 0.00
gpa_t2 7.08 0.88 0.14
gpa_t3 7.14 0.87 0.27
absences_t1 4.66 5.15 0.00
absences_t2 3.81 3.90 0.14
absences_t3 3.67 3.86 0.27
study_hours 6.01 2.59 0.00
screen_time 2.90 1.50 0.00
teacher_rating_effort 50.00 7.98 0.00

4.3 Missingness by variable block

Code 
missing_by_construct <- codebook |>
  group_by(construct) |>
  summarise(
    n_variables = n(),
    mean_missing_rate = mean(missing_rate, na.rm = TRUE),
    max_missing_rate = max(missing_rate, na.rm = TRUE),
    .groups = "drop"
  ) |>
  arrange(desc(mean_missing_rate))

kable(missing_by_construct, digits = 3)
construct n_variables mean_missing_rate max_missing_rate
school_anxiety 18 0.263 0.530
academic_self_efficacy 15 0.211 0.437
school_belonging 15 0.208 0.553
attention_regulation 4 0.106 0.106
observed_academic_behavioural 12 0.069 0.274
mastery_goal_orientation 5 0.049 0.060
teacher_support 5 0.047 0.055
academic_reasoning_ability 12 0.036 0.044
demographics 10 0.004 0.020
cluster_context 7 0.000 0.000
missing_data_design 6 0.000 0.000

4.4 Longitudinal dropout and incomplete data

Code 
dropout_overview <- dat |>
  summarise(
    dropout_t2 = mean(dropout_t2, na.rm = TRUE),
    dropout_t3 = mean(dropout_t3, na.rm = TRUE),
    missing_any_t1 = mean(missing_any_t1, na.rm = TRUE),
    missing_any_t2 = mean(missing_any_t2, na.rm = TRUE),
    missing_any_t3 = mean(missing_any_t3, na.rm = TRUE)
  ) |>
  pivot_longer(
    everything(),
    names_to = "indicator",
    values_to = "proportion"
  )

kable(dropout_overview, digits = 3)
indicator proportion
dropout_t2 0.138
dropout_t3 0.274
missing_any_t1 0.817
missing_any_t2 0.853
missing_any_t3 0.869

5 Research questions

The questions below are written as substantive questions, not as statistical instructions. Treat them as a project brief or as the starting point for a preregistration. You should decide which variables, scores, models, and assumptions are appropriate.

5.1 Cross-sectional research questions

The cross-sectional part uses baseline information only.

5.1.1 RQ1. Socioeconomic background and academic achievement

Is socioeconomic status associated with baseline academic achievement?

H1. Higher socioeconomic status is expected to be associated with higher baseline academic achievement.

5.1.2 RQ2. Socioeconomic background, ability, and self-efficacy

Are academic reasoning ability and academic self-efficacy plausible psychological pathways linking socioeconomic status with academic achievement?

H2. Higher socioeconomic status is expected to be associated with stronger academic reasoning ability and stronger academic self-efficacy. Academic reasoning ability and academic self-efficacy are expected to be positively associated with baseline academic achievement.

5.1.3 RQ3. Academic self-efficacy and academic functioning

Is academic self-efficacy associated with better academic functioning at baseline?

H3. Higher academic self-efficacy is expected to be associated with higher GPA, more frequent homework completion, more study hours, and higher teacher-rated effort.

5.1.4 RQ4. Teacher support, belonging, and school anxiety

Is perceived teacher support associated with lower school anxiety, and is this association partly explained by school belonging?

H4. Stronger perceived teacher support is expected to be associated with stronger school belonging. Stronger school belonging is expected to be associated with lower school anxiety.

5.1.5 RQ5. School anxiety and academic functioning

Is school anxiety associated with poorer academic functioning at baseline?

H5. Higher school anxiety is expected to be associated with more absences and lower GPA. Its association with study hours may be weaker or less consistent.

5.1.6 RQ6. Mastery goal orientation and adaptive school engagement

Is mastery goal orientation associated with more adaptive school engagement?

H6. Higher mastery goal orientation is expected to be associated with stronger academic self-efficacy, more frequent homework completion, more study hours, and higher teacher-rated effort.

5.1.7 RQ7. Attention regulation and academic achievement

Is attention regulation associated with baseline academic achievement beyond motivational and emotional factors?

H7. Better attention regulation is expected to be positively associated with GPA and teacher-rated effort.

5.1.8 RQ8. Classroom and school context

Are classroom climate and school resources associated with perceived teacher support, school belonging, school anxiety, and academic achievement?

H8. More favourable classroom and school contexts are expected to be associated with stronger perceived teacher support, stronger school belonging, lower school anxiety, and higher academic achievement.

5.1.9 RQ9. Construct distinctiveness

Are academic self-efficacy, school anxiety, school belonging, mastery goal orientation, and perceived teacher support empirically distinguishable constructs?

H9. The constructs are expected to be related but not interchangeable. For example, academic self-efficacy and school anxiety should be negatively related, but they should not be treated as the same construct.

5.1.10 RQ10. Group differences in school adjustment

Do indicators of school adjustment and academic functioning differ by gender, school type, language background, or socioeconomic status?

H10. Some group differences are expected, but their size, direction, and substantive interpretation should be evaluated cautiously.

5.2 Longitudinal research questions

The longitudinal part uses repeated measurements of academic self-efficacy, school anxiety, school belonging, GPA, and absences across three waves.

5.2.1 LRQ1. Stability of school adjustment

How stable are academic self-efficacy, school anxiety, and school belonging across the three waves?

LH1. Academic self-efficacy, school anxiety, and school belonging are expected to show moderate-to-strong stability over time, but not perfect stability.

5.2.2 LRQ2. Mean-level change in school adjustment

Do average levels of academic self-efficacy, school anxiety, and school belonging change over time?

LH2. Average levels of academic self-efficacy and belonging are expected to be relatively stable. School anxiety may show more noticeable change and greater individual variability.

5.2.3 LRQ3. Belonging and later school anxiety

Does school belonging predict later school anxiety after taking earlier anxiety into account?

LH3. Higher school belonging at an earlier wave is expected to be associated with lower school anxiety at the following wave.

5.2.4 LRQ4. Academic self-efficacy and later achievement

Does academic self-efficacy predict later academic achievement after taking earlier achievement into account?

LH4. Higher academic self-efficacy at an earlier wave is expected to be associated with higher GPA at the following wave.

5.2.5 LRQ5. School anxiety and later academic functioning

Does school anxiety predict later GPA and absences after taking earlier academic functioning into account?

LH5. Higher school anxiety at an earlier wave is expected to be associated with more later absences and lower later GPA.

5.2.6 LRQ6. Reciprocal relations between academic self-efficacy and achievement

Are academic self-efficacy and GPA reciprocally related over time?

LH6. Higher self-efficacy is expected to predict later GPA, and higher GPA is expected to predict later self-efficacy. The two directions may differ in magnitude.

5.2.7 LRQ7. Change in self-efficacy and change in GPA

Are individuals who increase in academic self-efficacy also more likely to improve in GPA?

LH7. Increases in academic self-efficacy are expected to be associated with more favourable academic trajectories.

5.2.8 LRQ8. Persistent school anxiety

Are individuals with persistently high school anxiety more likely to show unfavourable academic trajectories?

LH8. Persistent school anxiety is expected to be associated with more absences and lower GPA over time.

5.2.9 LRQ9. Differences in longitudinal patterns across groups

Do longitudinal patterns differ by socioeconomic status, gender, school type, or language background?

LH9. Some differences in initial levels and trajectories are expected across groups, but these differences should be interpreted in relation to measurement quality, missing data, and baseline differences.

5.2.10 LRQ10. Attrition and follow-up participation

Are individuals with incomplete follow-up data different from individuals with more complete data?

LH10. Incomplete follow-up data may be associated with baseline achievement, school anxiety, absences, and socioeconomic status.

6 Optional analysis routes and suggested solutions

This section gives possible analysis routes. It is not part of the research-question statement. Use it after you have translated the substantive questions into your own analysis plan.

How to use this section

The code below is deliberately written as a set of possible routes rather than as a required solution. You may answer some questions with sum scores and regressions, others with path models, and others with latent variable models. More complex models are not automatically better.

6.1 Prepare baseline scale scores

A defensible first pass is to create transparent scale scores. These scores are useful for descriptive summaries, correlations, simple regressions, and preliminary path models.

Code 
library(tidyverse)

dat_scores <- dat |>
  mutate(
    selfeff_t1_score = rowMeans(across(se1_t1:se5_t1), na.rm = TRUE),
    anxiety_t1_score = rowMeans(across(anx1_t1:anx6_t1), na.rm = TRUE),
    belong_t1_score = rowMeans(across(bel1_t1:bel5_t1), na.rm = TRUE),
    mastery_t1_score = rowMeans(across(mast1_t1:mast5_t1), na.rm = TRUE),
    teachsup_t1_score = rowMeans(across(ts1_t1:ts5_t1), na.rm = TRUE),
    ability_t1_score = rowMeans(across(abil1:abil12), na.rm = TRUE)
  ) |>
  mutate(
    across(
      c(att_acc, att_rt_inv, att_inhibit, att_switch),
      ~ as.numeric(scale(.x)),
      .names = "{.col}_z"
    ),
    attention_t1_score = rowMeans(
      across(c(att_acc_z, att_rt_inv_z, att_inhibit_z, att_switch_z)),
      na.rm = TRUE
    )
  )

A useful check is whether the expected associations appear in the zero-order correlations.

Code 
score_vars <- c(
  "ses", "gpa_t1", "absences_t1", "study_hours", "teacher_rating_effort",
  "selfeff_t1_score", "anxiety_t1_score", "belong_t1_score",
  "mastery_t1_score", "teachsup_t1_score", "ability_t1_score",
  "attention_t1_score"
)

cor(dat_scores[score_vars], use = "pairwise.complete.obs") |>
  round(2)

Expected broad pattern:

  • selfeff_t1_score, ability_t1_score, attention_t1_score, and ses should be positively associated with gpa_t1.
  • anxiety_t1_score should be positively associated with absences_t1 and negatively associated with gpa_t1.
  • teachsup_t1_score should be positively associated with belong_t1_score.
  • belong_t1_score should be negatively associated with anxiety_t1_score.

6.2 Simple regression solutions

6.2.1 RQ1: Socioeconomic status and GPA

Code 
m_rq1 <- lm(gpa_t1 ~ ses, data = dat_scores)
summary(m_rq1)

A minimal extension adds demographic and contextual covariates.

Code 
m_rq1_adj <- lm(
  gpa_t1 ~ ses + gender + language_home + school_type + school_resources,
  data = dat_scores
)

summary(m_rq1_adj)

6.2.2 RQ3 and RQ5: Self-efficacy, anxiety, and academic functioning

Code 
m_gpa <- lm(
  gpa_t1 ~ selfeff_t1_score + anxiety_t1_score + ses + ability_t1_score,
  data = dat_scores
)

m_abs <- glm(
  absences_t1 ~ anxiety_t1_score + belong_t1_score + ses,
  data = dat_scores,
  family = poisson()
)

summary(m_gpa)
summary(m_abs)

For absences_t1, inspect overdispersion before relying on a Poisson model.

Code 
sum(residuals(m_abs, type = "pearson")^2) / df.residual(m_abs)

6.3 Path-analysis solution with observed scale scores

A compact baseline path model can address several cross-sectional questions at once.

Code 
library(lavaan)

model_scores_cross <- '
  ability_t1_score ~ ses
  selfeff_t1_score ~ ability_t1_score + mastery_t1_score + teachsup_t1_score + ses
  belong_t1_score ~ teachsup_t1_score + ses
  anxiety_t1_score ~ selfeff_t1_score + belong_t1_score + ses
  gpa_t1 ~ ability_t1_score + selfeff_t1_score + anxiety_t1_score + attention_t1_score + ses
  absences_t1 ~ anxiety_t1_score + belong_t1_score + ses
'

fit_scores_cross <- sem(
  model_scores_cross,
  data = dat_scores,
  missing = "fiml",
  estimator = "MLR",
  cluster = "class_id"
)

summary(fit_scores_cross, fit.measures = TRUE, standardized = TRUE, rsquare = TRUE)

A more focused mediation model addresses the teacher support, belonging, and anxiety question.

Code 
model_scores_mediation <- '
  belong_t1_score ~ a * teachsup_t1_score + ses
  anxiety_t1_score ~ b * belong_t1_score + cprime * teachsup_t1_score + ses

  indirect := a * b
  total := cprime + indirect
'

fit_scores_mediation <- sem(
  model_scores_mediation,
  data = dat_scores,
  missing = "fiml",
  estimator = "MLR",
  cluster = "class_id"
)

summary(fit_scores_mediation, fit.measures = TRUE, standardized = TRUE)

6.4 Baseline latent-variable solution

After inspecting score-based results, you may represent the main constructs as latent variables. This is especially relevant when construct distinctiveness and measurement quality are part of the question.

Code 
model_cross_sectional <- '
  selfeff =~ se1_t1 + se2_t1 + se3_t1 + se4_t1 + se5_t1
  anxiety =~ anx1_t1 + anx2_t1 + anx3_t1 + anx4_t1 + anx5_t1 + anx6_t1
  belong  =~ bel1_t1 + bel2_t1 + bel3_t1 + bel4_t1 + bel5_t1
  teachsup =~ ts1_t1 + ts2_t1 + ts3_t1 + ts4_t1 + ts5_t1
  mastery =~ mast1_t1 + mast2_t1 + mast3_t1 + mast4_t1 + mast5_t1

  ability =~ abil1 + abil2 + abil3 + abil4 + abil5 + abil6 +
             abil7 + abil8 + abil9 + abil10 + abil11 + abil12

  attention =~ att_acc + att_rt_inv + att_inhibit + att_switch

  ability ~ ses
  selfeff ~ ability + mastery + teachsup + ses
  belong ~ teachsup + ses
  anxiety ~ selfeff + belong + ses
  gpa_t1 ~ ability + selfeff + anxiety + attention + ses
  absences_t1 ~ anxiety + belong + ses
'

ordered_items_t1 <- c(
  paste0("se", 1:5, "_t1"),
  paste0("anx", 1:6, "_t1"),
  paste0("bel", 1:5, "_t1"),
  paste0("mast", 1:5, "_t1"),
  paste0("ts", 1:5, "_t1"),
  paste0("abil", 1:12)
)

fit_cross <- sem(
  model_cross_sectional,
  data = dat,
  ordered = ordered_items_t1,
  estimator = "WLSMV"
)

summary(fit_cross, fit.measures = TRUE, standardized = TRUE, rsquare = TRUE)

Possible interpretation route:

  • Start with global fit: chi-square, CFI, TLI, RMSEA, and SRMR when available.
  • Inspect local diagnostics: residuals, modification indices, and unusually weak indicators.
  • Avoid adding parameters only because they improve fit.
  • Interpret indirect or structural paths only after the measurement part is defensible.

6.5 Longitudinal score-based solution

A first longitudinal pass can use scale scores. This keeps the focus on stability, change, and prospective associations.

Code 
dat_long_scores <- dat |>
  mutate(
    selfeff_t1_score = rowMeans(across(se1_t1:se5_t1), na.rm = TRUE),
    selfeff_t2_score = rowMeans(across(se1_t2:se5_t2), na.rm = TRUE),
    selfeff_t3_score = rowMeans(across(se1_t3:se5_t3), na.rm = TRUE),

    anxiety_t1_score = rowMeans(across(anx1_t1:anx6_t1), na.rm = TRUE),
    anxiety_t2_score = rowMeans(across(anx1_t2:anx6_t2), na.rm = TRUE),
    anxiety_t3_score = rowMeans(across(anx1_t3:anx6_t3), na.rm = TRUE),

    belong_t1_score = rowMeans(across(bel1_t1:bel5_t1), na.rm = TRUE),
    belong_t2_score = rowMeans(across(bel1_t2:bel5_t2), na.rm = TRUE),
    belong_t3_score = rowMeans(across(bel1_t3:bel5_t3), na.rm = TRUE)
  )

6.5.1 LRQ3: Belonging and later anxiety

Code 
m_lrq3 <- lm(
  anxiety_t2_score ~ anxiety_t1_score + belong_t1_score + ses + gender,
  data = dat_long_scores
)

summary(m_lrq3)

6.5.2 LRQ4 and LRQ5: Anxiety, self-efficacy, and later GPA

Code 
m_lrq4_lrq5 <- lm(
  gpa_t2 ~ gpa_t1 + selfeff_t1_score + anxiety_t1_score + ses,
  data = dat_long_scores
)

summary(m_lrq4_lrq5)

6.6 Longitudinal latent-variable solution

The following model is one possible latent longitudinal model. It should be fitted only after you have inspected the repeated measures and considered whether the indicators are comparable across time.

Code 
model_longitudinal <- '
  selfeff_t1 =~ se1_t1 + se2_t1 + se3_t1 + se4_t1 + se5_t1
  selfeff_t2 =~ se1_t2 + se2_t2 + se3_t2 + se4_t2 + se5_t2
  selfeff_t3 =~ se1_t3 + se2_t3 + se3_t3 + se4_t3 + se5_t3

  anxiety_t1 =~ anx1_t1 + anx2_t1 + anx3_t1 + anx4_t1 + anx5_t1 + anx6_t1
  anxiety_t2 =~ anx1_t2 + anx2_t2 + anx3_t2 + anx4_t2 + anx5_t2 + anx6_t2
  anxiety_t3 =~ anx1_t3 + anx2_t3 + anx3_t3 + anx4_t3 + anx5_t3 + anx6_t3

  selfeff_t2 ~ selfeff_t1
  selfeff_t3 ~ selfeff_t2

  anxiety_t2 ~ anxiety_t1
  anxiety_t3 ~ anxiety_t2

  gpa_t2 ~ gpa_t1
  gpa_t3 ~ gpa_t2

  anxiety_t2 ~ selfeff_t1
  anxiety_t3 ~ selfeff_t2

  gpa_t2 ~ selfeff_t1 + anxiety_t1
  gpa_t3 ~ selfeff_t2 + anxiety_t2

  selfeff_t1 ~~ anxiety_t1
  selfeff_t2 ~~ anxiety_t2
  selfeff_t3 ~~ anxiety_t3
'

ordered_items_long <- c(
  paste0("se", 1:5, "_t1"), paste0("se", 1:5, "_t2"), paste0("se", 1:5, "_t3"),
  paste0("anx", 1:6, "_t1"), paste0("anx", 1:6, "_t2"), paste0("anx", 1:6, "_t3")
)

fit_long <- sem(
  model_longitudinal,
  data = dat,
  ordered = ordered_items_long,
  estimator = "WLSMV"
)

summary(fit_long, fit.measures = TRUE, standardized = TRUE, rsquare = TRUE)

6.7 Checking incomplete follow-up data

The attrition question can be addressed descriptively before any longitudinal model is fitted.

Code 
dat |>
  group_by(dropout_t3) |>
  summarise(
    n = n(),
    mean_gpa_t1 = mean(gpa_t1, na.rm = TRUE),
    mean_absences_t1 = mean(absences_t1, na.rm = TRUE),
    mean_ses = mean(ses, na.rm = TRUE),
    .groups = "drop"
  )

If you create baseline school-adjustment scores, also compare baseline anxiety, self-efficacy, and belonging by follow-up completion status.

Code 
dat_long_scores |>
  group_by(dropout_t3) |>
  summarise(
    n = n(),
    selfeff_t1 = mean(selfeff_t1_score, na.rm = TRUE),
    anxiety_t1 = mean(anxiety_t1_score, na.rm = TRUE),
    belong_t1 = mean(belong_t1_score, na.rm = TRUE),
    .groups = "drop"
  )

7 Missing data and clustering

7.1 Missing data

The dataset contains missing data by design. Missingness occurs at several levels:

  • item-level missingness in questionnaire and reasoning indicators;
  • block-level missingness for the attention task;
  • planned missingness for some questionnaire forms;
  • longitudinal dropout at later waves.

Report how missing data were handled. Also report whether your conclusions change when you compare different defensible approaches, such as complete-case analysis, full-information maximum likelihood, multiple imputation, or categorical-data estimators.

7.2 Clustering

The observations are not fully independent: individuals are nested in classes and schools. Some constructs, especially teacher support, belonging, and GPA, may show class-level or school-level dependence.

At minimum, inspect whether conclusions are sensitive to classroom clustering. For example, compare a model that ignores clustering with one that adjusts standard errors for class_id, when the estimator and model type allow this.

Code 
fit_clustered <- sem(
  model_scores_mediation,
  data = dat_scores,
  missing = "fiml",
  estimator = "MLR",
  cluster = "class_id"
)

summary(fit_clustered, fit.measures = TRUE, standardized = TRUE)

8 Reporting checklist

For each analysis, report:

  • the research question being addressed;
  • how each construct was represented;
  • inclusion and exclusion criteria;
  • treatment of missing data;
  • whether clustering was ignored, adjusted, or modelled;
  • estimator and assumptions, when applicable;
  • global model fit, if a model with fit indices was estimated;
  • local diagnostics, if relevant;
  • estimates with uncertainty intervals or standard errors;
  • a substantive interpretation that distinguishes statistical evidence, model fit, and causal claims.