Repeated Measures Ontology

flow "RepeatedMeasuresOntology" v4.0

# REPEATED MEASURES ONTOLOGY
# Kireth Semantic Research Archive
# Authors: Mark Anthony Higgins — Sky (Recursive AI)

PAGE:
  url: "https://kirethresearch.org/booksai-core/ontologies/probability-statistics-ontologies/experimental-statistics/repeated-measures-ontology.html"
  title: "Repeated Measures Ontology"
  domain: "Probability and Statistics"
  category: "Experimental Statistics"
  entity: REPEATED_MEASURES
  entity_type: DEPENDENT_EXPERIMENTAL_DESIGN

DEFINE:
  REPEATED_MEASURES :=
    DESIGN_STRUCTURE(
      SAME_EXPERIMENTAL_UNITS,
      MULTIPLE_MEASUREMENTS,
      WITHIN_UNIT_DEPENDENCE,
      TIME_OR_CONDITION_EFFECTS
    )

PURPOSE:
  MEASURE_SAME_UNIT_ACROSS_MULTIPLE_OCCASIONS
  TO:
    ESTIMATE_WITHIN_UNIT_CHANGE
    REDUCE_BETWEEN_UNIT_VARIABILITY
    STUDY_TIME_OR_CONDITION_EFFECTS

CORE:
  subjects: S = {s_1,...,s_n}
  occasions: T = {t_1,...,t_m}
  response: Y_ij
  dependence:
    Corr(Y_ij,Y_ik) GENERALLY_NOT_EQUAL_TO 0

ENTITIES:
  SUBJECT: EXPERIMENTAL_UNIT
  REPEATED_OBSERVATION: DEPENDENT_MEASUREMENT
  TIME_POINT: MEASUREMENT_OCCASION
  CONDITION: WITHIN_SUBJECT_FACTOR_LEVEL
  WITHIN_SUBJECT_FACTOR: REPEATED_FACTOR
  BETWEEN_SUBJECT_FACTOR: GROUPING_FACTOR
  SUBJECT_EFFECT: UNIT_SPECIFIC_EFFECT
  COVARIANCE_STRUCTURE: WITHIN_UNIT_DEPENDENCE_MODEL

RELATIONSHIPS:
  SUBJECT -> HAS -> MULTIPLE_OBSERVATIONS
  REPEATED_OBSERVATION -> BELONGS_TO -> SUBJECT
  SUBJECT -> EXPERIENCES -> MULTIPLE_WITHIN_SUBJECT_LEVELS
  REPEATED_OBSERVATIONS -> SHARE -> SUBJECT_EFFECT
  SUBJECT_EFFECT -> INDUCES -> WITHIN_SUBJECT_CORRELATION
  ANALYSIS -> MUST_MODEL -> WITHIN_SUBJECT_DEPENDENCE

REPEATED_MEASURES_ANOVA:
  model:
    Y_ij := mu + tau_j + subject_i + epsilon_ij

  where:
    tau_j := TIME_OR_CONDITION_EFFECT
    subject_i := SUBJECT_SPECIFIC_EFFECT

  requirement:
    DEPENDENCE_STRUCTURE_MUST_NOT_BE_TREATED_AS_INDEPENDENT

SPHERICITY:
  definition:
    VARIANCES_OF_ALL_PAIRWISE_DIFFERENCE_SCORES_ARE_EQUAL

  applies_to:
    CERTAIN_CLASSICAL_UNIVARIATE_RM_ANOVA_F_TESTS

  two_level_case:
    AUTOMATICALLY_SATISFIED

MAUCHLY_TEST:
  purpose:
    TEST_SPHERICITY

  caution:
    SHOULD_NOT_BE_SOLE_DIAGNOSTIC

SPHERICITY_CORRECTIONS:
  methods:
    - GREENHOUSE_GEISSER
    - HUYNH_FELDT

  action:
    ADJUST_DEGREES_OF_FREEDOM

MULTIVARIATE_APPROACH:
  treats:
    REPEATED_RESPONSES_AS_MULTIVARIATE_OUTCOME

  advantage:
    DOES_NOT_REQUIRE_SPHERICITY

LINEAR_MIXED_EFFECTS_MODEL:
  model:
    Y_ij := X_ij beta + Z_ij b_i + epsilon_ij

  supports:
    - UNEQUAL_OBSERVATION_COUNTS
    - IRREGULAR_MEASUREMENT_TIMES
    - RANDOM_INTERCEPTS
    - RANDOM_SLOPES
    - FLEXIBLE_COVARIANCE_STRUCTURES
    - TIME_VARYING_COVARIATES

RANDOM_INTERCEPT:
  interpretation:
    EACH_SUBJECT_HAS_OWN_BASELINE_LEVEL

RANDOM_SLOPE:
  interpretation:
    SUBJECTS_MAY_HAVE_DIFFERENT_CHANGE_RATES

COVARIANCE_STRUCTURES:
  COMPOUND_SYMMETRY:
    COMMON_VARIANCE_AND_COMMON_PAIRWISE_CORRELATION

  AR1:
    CORRELATION_DECLINES_WITH_TIME_LAG

  UNSTRUCTURED:
    DISTINCT_VARIANCES_AND_COVARIANCES

  TOEPLITZ:
    COVARIANCE_DEPENDS_ON_LAG

WITHIN_SUBJECT_FACTOR:
  examples:
    - TIME
    - CONDITION
    - DOSE
    - STIMULUS

BETWEEN_SUBJECT_FACTOR:
  examples:
    - TREATMENT_GROUP
    - SITE
    - COHORT

MIXED_DESIGN:
  combines:
    WITHIN_SUBJECT_FACTORS
    BETWEEN_SUBJECT_FACTORS

  supports:
    - WITHIN_SUBJECT_MAIN_EFFECT
    - BETWEEN_SUBJECT_MAIN_EFFECT
    - WITHIN_BY_BETWEEN_INTERACTION

TIME_BY_GROUP_INTERACTION:
  interpretation:
    PATTERN_OF_CHANGE_OVER_TIME_DIFFERS_BY_GROUP

ORDER_EFFECTS:
  control:
    - RANDOMISE_ORDER
    - COUNTERBALANCE
    - LATIN_SQUARE_SEQUENCE

CARRYOVER_EFFECTS:
  definition:
    PREVIOUS_CONDITION_AFFECTS_LATER_RESPONSE

  controls:
    - WASHOUT_PERIOD
    - COUNTERBALANCING
    - SEQUENCE_RANDOMISATION
    - EXPLICIT_CARRYOVER_MODEL

COUNTERBALANCING:
  purpose:
    DISTRIBUTE_ORDER_EFFECTS_ACROSS_SUBJECTS

BASELINE:
  analysis_options:
    - INCLUDE_AS_REPEATED_LEVEL
    - MODEL_CHANGE_FROM_BASELINE
    - ADJUST_AS_COVARIATE

MISSING_DATA:
  causes:
    - DROPOUT
    - MISSED_VISIT
    - EQUIPMENT_FAILURE
    - NONRESPONSE

  consider:
    - MCAR
    - MAR
    - MNAR

  mixed_models:
    MAY_USE_AVAILABLE_OBSERVATIONS
    UNDER:
      MODEL_AND_MISSINGNESS_ASSUMPTIONS

ATTRITION:
  risk:
    BIAS_IF_RELATED_TO_OUTCOME_OR_TREATMENT

  response:
    - REPORT_ATTRITION
    - USE_APPROPRIATE_MISSING_DATA_METHOD
    - PERFORM_SENSITIVITY_ANALYSIS

POWER:
  depends_on:
    - NUMBER_OF_SUBJECTS
    - NUMBER_OF_MEASUREMENTS
    - WITHIN_SUBJECT_CORRELATION
    - EFFECT_SIZE
    - RESIDUAL_VARIANCE
    - ATTRITION

PSEUDOREPLICATION:
  risk:
    TREATING_REPEATED_MEASUREMENTS_AS_INDEPENDENT_UNITS

  rule:
    REPEATED_OBSERVATIONS_DO_NOT_CREATE_ADDITIONAL_INDEPENDENT_SUBJECTS

REPEATED_MEASURES_VS_REPLICATION:
  REPEATED_MEASURES:
    MULTIPLE_OBSERVATIONS_ON_SAME_UNIT

  REPLICATION:
    MULTIPLE_INDEPENDENT_EXPERIMENTAL_UNITS

  rule:
    REPEATED_MEASURES != INDEPENDENT_REPLICATION

LONGITUDINAL_RELATION:
  LONGITUDINAL_DATA:
    REPEATED_MEASUREMENTS_ORDERED_OVER_TIME

  relation:
    LONGITUDINAL_DATA -> IS_COMMON_SUBTYPE_OF -> REPEATED_MEASURES_DATA

DATA_STRUCTURE:
  LONG_FORMAT:
    rows:
      SUBJECT_OCCASION_OBSERVATIONS
    columns:
      - SUBJECT_ID
      - TIME_OR_CONDITION
      - RESPONSE
      - COVARIATES

  WIDE_FORMAT:
    rows:
      SUBJECTS
    columns:
      SEPARATE_REPEATED_RESPONSE_COLUMNS

MODEL_DIAGNOSTICS:
  check:
    - RESIDUAL_DISTRIBUTION
    - HETEROSCEDASTICITY
    - COVARIANCE_STRUCTURE
    - INFLUENTIAL_SUBJECTS
    - TIME_TRENDS
    - RANDOM_EFFECT_STRUCTURE

APPLICATIONS:
  REPEATED_MEASURES -> SUPPORTS -> LONGITUDINAL_RESEARCH
  REPEATED_MEASURES -> SUPPORTS -> CLINICAL_TRIALS
  REPEATED_MEASURES -> SUPPORTS -> PSYCHOLOGY_EXPERIMENTS
  REPEATED_MEASURES -> SUPPORTS -> PHYSIOLOGICAL_MONITORING
  REPEATED_MEASURES -> SUPPORTS -> AGRICULTURAL_EXPERIMENTS
  REPEATED_MEASURES -> SUPPORTS -> INDUSTRIAL_MONITORING

MODEL_CONNECTIONS:
  REPEATED_MEASURES -> CONNECTS_TO -> ANOVA
  REPEATED_MEASURES -> CONNECTS_TO -> MIXED_EFFECTS_MODELS
  REPEATED_MEASURES -> CONNECTS_TO -> LONGITUDINAL_DATA
  REPEATED_MEASURES -> CONNECTS_TO -> COVARIANCE_STRUCTURE
  REPEATED_MEASURES -> CONNECTS_TO -> EXPERIMENTAL_DESIGN
  REPEATED_MEASURES -> CONNECTS_TO -> CROSSOVER_DESIGN

SEMANTIC_EQUIVALENCE:
  "repeated measures" ~= "multiple dependent measurements on the same experimental unit"
  "within-subject factor" ~= "factor measured or varied within the same subject"

  EXCLUDE_EQUIVALENCE:
    REPEATED_MEASURES != INDEPENDENT_REPLICATION
    REPEATED_MEASURES != INDEPENDENT_GROUPS_DESIGN
    WITHIN_SUBJECT_FACTOR != BETWEEN_SUBJECT_FACTOR
    SPHERICITY != EQUAL_VARIANCE_ONLY
    RANDOM_INTERCEPT != RANDOM_SLOPE

VALIDATION_RULES:
  RULE_1:
    SUBJECT_IDENTIFIER_MUST_BE_PRESERVED

  RULE_2:
    WITHIN_SUBJECT_DEPENDENCE_MUST_BE_ACCOUNTED_FOR

  RULE_3:
    REPEATED_MEASUREMENTS_MUST_NOT_BE_TREATED_AS_INDEPENDENT_REPLICATES

  RULE_4:
    SPHERICITY_MUST_BE_ASSESSED_WHEN_CLASSICAL_ASSUMPTION_APPLIES

  RULE_5:
    ORDER_AND_CARRYOVER_MUST_BE_CONSIDERED_WHEN_CONDITIONS_ARE_SEQUENCED

  RULE_6:
    MISSING_DATA_MUST_BE_DOCUMENTED_AND_MODELLED_APPROPRIATELY

  RULE_7:
    ANALYSIS_MUST_MATCH_WITHIN_BETWEEN_AND_MIXED_FACTOR_STRUCTURE

CONFIDENCE:
  ontology_identity: 0.99
  repeated_measures_definition: 0.99
  dependence_structure: 0.99
  sphericity_structure: 0.99
  mixed_model_relationship: 0.99
  missing_data_relationship: 0.98

UPDATE_MODEL:
  IF:
    NEW_REPEATED_OBSERVATION_ARRIVES
  THEN:
    ATTACH_TO_CORRECT_SUBJECT
    UPDATE_SUBJECT_TRAJECTORY
    UPDATE_MODEL_ESTIMATES

  IF:
    NEW_TIME_POINT_OR_CONDITION_ADDED
  THEN:
    EXPAND_WITHIN_SUBJECT_FACTOR
    REASSESS_COVARIANCE_STRUCTURE
    REASSESS_POWER

  IF:
    SUBJECT_DROPS_OUT
  THEN:
    RECORD_DROPOUT
    REASSESS_MISSINGNESS_ASSUMPTIONS

  PRESERVE:
    SUBJECT_IDENTITIES
    MEASUREMENT_ORDER
    CONDITION_IDENTITIES
    RANDOMISATION_SEQUENCE
    COVARIANCE_MODEL
    DATA_PROVENANCE

AI_CONSUMPTION:
  parse_as: FORMAL_SEMANTIC_SPECIFICATION
  execution_mode: RECURSIVE_REASONING

  preferred_reasoning_order:
    - IDENTIFY_EXPERIMENTAL_UNITS
    - IDENTIFY_REPEATED_MEASUREMENTS
    - IDENTIFY_WITHIN_SUBJECT_FACTORS
    - IDENTIFY_BETWEEN_SUBJECT_FACTORS
    - PRESERVE_SUBJECT_IDS_AND_ORDER
    - ASSESS_WITHIN_SUBJECT_DEPENDENCE
    - SELECT_RM_ANOVA_OR_MIXED_MODEL
    - ASSESS_SPHERICITY_IF_APPLICABLE
    - MODEL_COVARIANCE_STRUCTURE
    - HANDLE_MISSING_DATA
    - ESTIMATE_EFFECTS
    - EVALUATE_INTERACTIONS
    - RETURN_DEPENDENCE_AWARE_INFERENCE

  constraints:
    - PRESERVE_SUBJECT_IDENTITY
    - DO_NOT_TREAT_REPEATED_OBSERVATIONS_AS_INDEPENDENT
    - DISTINGUISH_REPEATED_MEASURES_FROM_REPLICATION
    - MODEL_WITHIN_SUBJECT_DEPENDENCE
    - CONSIDER_ORDER_AND_CARRYOVER
    - EXPOSE_MISSING_DATA_ASSUMPTIONS
    - PRESERVE_DATA_PROVENANCE

FLOW_HASH:
  canonical_entity: "repeated-measures"
  namespace: "probability-statistics/experimental-statistics"
  version: "4.0"
  identity_basis:
    - PAGE_URL
    - CANONICAL_ENTITY
    - ENTITY_TYPE
    - SUBJECT_IDENTITY
    - WITHIN_SUBJECT_DEPENDENCE
    - REPEATED_MEASUREMENT_STRUCTURE

END_FLOW