Package {lambdastar}

Lambda Star: measurement, linear hypotheses and percentile intervals

Description

A standalone R package for parallel measurements, nuisance-adjusted linear models, the numerical parsimony functional and ordinary case/cluster percentile intervals. Use lambda_measure(), lambda_model() and lambda_compare(). The manuscript estimator is the default; an alternative population estimator is explicitly selectable. Points and bootstrap draws use the same selected statistic. See lambda_inference. lambda_design() binds a reusable encoded model to its input rows; lambda_hypothesis() selects target terms conditional on explicit adjustment terms. lambda_contrast() encodes named homogeneous coefficient restrictions; lambda_marginal_contrast() uses explicit predictor settings and weights. Design constructors support fixed or reevaluated bootstrap basis recipes. The manuscript path assumes stable structure plus zero-mean homogeneous, isotropic background fluctuation with finite second moments. Neither Gaussian responses nor equal total group variances are required. The measurement assumption is used, not established by fitting. The optional population estimator has additional assumptions described in lambda_inference. An installed example is available at system.file("examples", "quickstart.R", package = "lambdastar"). A guided lesson with plots, known simulated signal and editable experiments is at system.file("doc", "LEARN_LAMBDASTAR.md", package = "lambdastar"). Source system.file("examples", "learn_lambdastar.R", package = "lambdastar") and call lambdastar_tutorial() to create a personal worked example. The centered fixed-model learning path and supported-scope table are at system.file("doc", "MODEL_SPACE_WORKFLOW.md", package = "lambdastar"). It links reusable designs, conditional effects, coefficient/grid contrasts, basis policies and the distinction between fixed-profile and population targets. Source system.file("examples", "intervals_and_targets.R", package="lambdastar") and call lambdastar_intervals_example() for regular and weak-signal percentile examples (B=5000, 95%, seed=1), with actual draws and undefined-value diagnostics. lambda_reference() retains a known reference origin and mean direction; lambda_paired() evaluates after-minus-before parallel measurement pairs. The derivation and resolution conventions are in installed doc/REFERENCE_MEANS.md. lambda_panel() encodes fixed person-by-occasion designs with parallel items, explicit person adjustment and whole-person bootstrap with distinct copies. Its derivation and runnable lesson are in installed doc/PANEL_MODELS.md. General covariance/mixed models and uncertainty in an estimated reference remain separate extensions. Ordinary centered calls keep their existing meaning. T_q is supplied on the composite-mean response scale. Measurements must be already scored; the package does not perform imputation or validate a scale.

Author(s)

Maintainer: Mike Hammes mike.hammes@mikehammes.name [copyright holder]

Authors:

• Mike Hammes mike.hammes@mikehammes.name [copyright holder]

Center a numeric matrix

Description

Center a numeric matrix

Usage

center_columns(x, name = "x")

Arguments

Value

Matrix centered by column, retaining row and column names.

Extract Lambda Star percentile intervals

Description

The stored confidence level is used when level is omitted. A different level requires keep_draws=TRUE and reuses the same parameter draws without resampling. The diagnostics attribute includes estimates, valid/undefined draw counts and explicit statuses for missing intervals. Conditional quantiles are available separately in object$bootstrap$conditional_quantiles. See lambda_inference.

Usage

## S3 method for class 'lambda_measurement'
confint(object, parm, level = 0.95, ...)

## S3 method for class 'lambda_model'
confint(object, parm, level = 0.95, ...)

## S3 method for class 'lambda_comparison'
confint(object, parm, level = 0.95, ...)

Arguments

Value

A lambda_ci matrix with lower/upper columns, diagnostics and inference attributes. Suppressed intervals contain NA and an explicit status.

Encoded design volume

Description

Encoded design volume

Usage

design_volume(x, logarithm = FALSE, control = lambda_control())

Arguments

Value

Scalar volume, or log volume. Null and one-direction models have V=1.

Estimate the noncentrality partition for an explicit design

Description

Estimate the noncentrality partition for an explicit design

Usage

estimate_lambda_partition_items(
  items,
  x,
  scale = c("composite_mean", "item"),
  control = lambda_control(),
  row_ids = NULL,
  nuisance = NULL,
  reference = NULL
)

Arguments

Value

Measurement state extended with raw and constrained partitions, degrees of freedom, observed energies and the encoded basis. The raw partition preserves additivity; the constrained partition caps captured structure at the nonnegative total. Kappa is NA when total structure is zero.

Estimate intrinsic structure from parallel measurements

Description

Measurements must target the same stable profile with independent, homogeneous replicate errors. Homogeneous isotropic fluctuation refers to measurement errors, not the total response variance within groups. Finite second moments are required; a Gaussian response distribution is not required for these moment/projection calculations. Complete, already scored items are required; neither reverse scoring nor missing-value substitution is inferred.

Usage

estimate_lambda_star_items(
  items,
  scale = c("composite_mean", "item"),
  row_ids = NULL,
  nuisance = NULL,
  control = lambda_control(),
  reference = NULL
)

Arguments

Value

Measurement state containing temperature, raw and constrained signal and noncentrality, retained composite profile and row identity. At zero temperature, status is singular_temperature and normalized estimates are NA. composite_response always refers to the mean; item scale only changes the noncentrality denominator, not this observed response.

Smooth capacity approximation and geometric activation

Description

Smooth capacity approximation and geometric activation

Usage

eta_app(temperature, resolution)

xi_eta_app(temperature, resolution)

geometry_activation(temperature, resolution)

xi_a(temperature, resolution)

Arguments

Value

Numeric values. eta_app is a labeled approximation, xi_eta_app its primitive, geometry_activation the Hill profile and xi_a its primitive. Zero-temperature values are mathematical boundary values only.

Quantized maximum-entropy capacity

Description

Numerically solves the Gibbs distribution over nearest-bin quantizer costs c_j = (abs(j) - 1/2)^2 for nonzero j, with c_0 = 0. The target minimum second moment is T/(12 T_q). This evaluates the defining supremum; it is not the entropy of a fitted Gaussian distribution. A log-moment equation avoids premature convergence at small positive temperatures.

Usage

eta_numerical(
  temperature,
  resolution,
  control = lambda_control(),
  details = FALSE
)

Arguments

Value

Numeric capacity in nats, or diagnostics with one row per coordinate. The value at zero is the mathematical boundary, not an inferential estimate.

Construct a centered hypothesis basis

Description

The returned X retains the encoded design. Q is used only for projection. Rank is tested after column normalization, making the decision insensitive to changes in predictor units. Redundant or constant columns are rejected.

Usage

hypothesis_basis(x, control = lambda_control())

Arguments

Value

List containing X, orthonormal Q, rank, log_volume, volume and control. log_volume is retained even when exponentiation underflows.

Settings for case or cluster percentile bootstrap intervals

Description

Defaults are 5000 draws, 95 percent two-sided percentile intervals and seed 1. Whole persons and predictors are resampled together. Every draw uses the same selected estimator as the original data. Undefined values are retained as NA; draws are never replaced. Any invalid draw suppresses the affected regular CI. Optional quantiles conditional on valid draws are returned in a separate table.

Usage

lambda_bootstrap_control(
  B = 5000L,
  conf.level = 0.95,
  ci.sides = "two.sided",
  ci.method = "percentile",
  resampling = "case",
  strata = NULL,
  seed = 1L,
  min_valid = 200L,
  conditional_quantiles = FALSE,
  keep_draws = FALSE,
  keep_indices = FALSE,
  cluster = NULL,
  percentile_interpolation = "boot"
)

Arguments

Value

Settings for the bootstrap argument of lambda_measure(), lambda_model() or lambda_compare().

Compare two models on one common measurement matrix

Description

This wrapper prepares the measurement state and case selection once and calls the same single-model evaluator twice. No separate F_H formula is used. Complete-case selection spans indicators and variables from BOTH models. delta_F is F_Hb - F_Ha; negative values mean the second model has lower F_H. This is a descriptive difference, not a p-value or automatic model selection.

Usage

lambda_compare(
  data,
  model_a,
  model_b,
  indicators,
  T_q,
  measurement_scale = c("mean", "item"),
  na.action = c("fail", "complete"),
  contrasts_a = NULL,
  contrasts_b = NULL,
  capacity = c("numerical", "smooth"),
  numerical_control = lambda_control(),
  eta_lookup = NULL,
  response_tol = sqrt(.Machine$double.eps),
  bootstrap = FALSE,
  estimator = c("paper", "population"),
  nuisance = NULL,
  nuisance_contrasts = NULL
)

Arguments

Value

A lambda_comparison with model_a, model_b, delta_F, shared measurement, case provenance and effective settings. At T=0 delta_F is NA.

Encode a homogeneous linear coefficient hypothesis

Description

Constructs L beta = 0 in the non-intercept coefficient coding of a full model. Named columns not supplied in L receive zero weights. The full design must be identifiable after common nuisance adjustment, and L must have independent rows. Intercept/nonzero-reference hypotheses require a different reference space and are not part of this constructor.

Usage

lambda_contrast(
  data,
  model,
  L,
  contrasts = NULL,
  nuisance = NULL,
  nuisance_contrasts = NULL,
  encoding = c("reevaluate", "fixed")
)

Arguments

Details

The null-model directions become additional nuisance columns. Consequently, lambda_star and kappa describe structure after adjustment for that null model. The actual ordered contrast coding is retained for F_H, not replaced by the numerical orthogonal basis. Geometry and estimability are rebuilt each draw.

Value

A lambda_design for the conditional contrast space. The realized L, coefficient right inverse, null basis and full-model metadata are available in the evaluated result's model component.

Examples

d <- data.frame(x=seq_len(20), z=sin(seq_len(20)))
lambda_contrast(d, ~x+z, c(x=1, z=-1))

Numerical settings for the Lambda Star core

Description

Numerical settings for the Lambda Star core

Usage

lambda_control(
  rank_tol = 1e-10,
  capacity_tol = 1e-10,
  tail_tol = 1e-14,
  integration_rel_tol = 1e-08,
  integration_abs_tol = 0,
  subdivisions = 200L,
  lookup_rel_tol = 1e-05,
  lookup_abs_tol = 0,
  lookup_max_points = 32769L,
  max_support = 1000000L
)

Arguments

Value

A validated list of numerical controls. Lookup error estimates are numerical estimates, not rigorous error certificates.

Bind a reusable encoded model specification to input rows

Description

A design keeps the actual coding and its recipe, not just a projection basis. Formula realization is deferred until common case selection in lambda_model() or lambda_compare(). Explicit matrices are already encoded. No temperature, fitted projection or measurement state is cached in this object.

Usage

lambda_design(
  data,
  model,
  contrasts = NULL,
  nuisance = NULL,
  nuisance_contrasts = NULL,
  encoding = c("reevaluate", "fixed")
)

## S3 method for class 'lambda_design'
print(x, ...)

Arguments

Details

Relevant input columns and row identities are bound exactly. New measurements on the same predictors are allowed for one-sided formulas; changed predictors or row order require a new design. Ordinary deterministic base/stats terms and supported namespace-qualified terms are portable; caller-defined functions must be evaluated explicitly into a matrix before construction.

Factor contrast defaults are recorded and realized as numeric contrasts. During bootstrap, explicit matrices and simple formulas are sliced by row; sample-dependent formula transforms are reevaluated by default, as with the existing formula interface. With encoding="fixed", the raw encoding learned after common case selection is retained during resampling. Projections are rebuilt in either case.

Value

A versioned lambda_design specification. X_H is populated for matrix inputs; formula matrices are available as encoded_x on the evaluated result. B stores the nuisance recipe. row_ids and bound_data record the input binding.

See Also

lambda_hypothesis(), lambda_contrast(), lambda_marginal_contrast(). The installed learning path is at system.file("doc", "MODEL_SPACE_WORKFLOW.md", package="lambdastar").

Examples

d <- data.frame(g=factor(rep(c("a", "b"), each=10)), x=seq_len(20))
design <- lambda_design(d, ~g+x)
design

Construct a conditional block from full-model terms

Description

Target and adjustment terms are explicit, disjoint selections from the full model's term labels. Columns are taken from that model's actual coding. Unselected terms are reported as omitted, although their variables still participate in full-recipe evaluation and common case selection.

Usage

lambda_hypothesis(
  data,
  model,
  target,
  adjust,
  contrasts = NULL,
  nuisance = NULL,
  nuisance_contrasts = NULL,
  encoding = c("reevaluate", "fixed")
)

Arguments

Details

The resulting lambda_star and kappa refer to structure remaining after the specified adjustment. Partial kappas with different adjustment spaces are not an additive partition. F_H comparisons require the same nuisance recipe. This is a term-block constructor, not a general coefficient restriction or an automatic Type I/II/III analysis. The intercept is always removed.

Value

A lambda_design for the target block with its effective nuisance recipe, target, adjustment and omitted-term metadata.

Examples

d <- data.frame(g=factor(rep(c("a","b"), each=10)), x=seq_len(20))
lambda_hypothesis(d, ~g*x, target="g:x", adjust=c("g","x"))

Estimator selection and ordinary percentile bootstrap

Description

estimator="paper" is the default. With nuisance design B (including an intercept), let d=N-rank(B), p=rank(M_B X_H), y=M_B Y_mean and Q_H its captured energy. On the mean scale, raw estimates are lambda_star=||y||^2/T-d, lambda_h=Q_H/T-p and lambda_perp=RSS/T-(d-p). T is the parallel-item disagreement divided by d*(K-1)*K. Item scale changes the denominator, retaining the composite-mean bath correction. Estimates constrain total signal to be nonnegative and captured signal to lie between zero and total.

Details

The selected points are in estimates and the top-level lambda/kappa fields. rho_star is lambda_star/(lambda_star+d) for the selected estimator. paper retains the manuscript estimates and raw values. inference and settings identify the estimator independently of whether bootstrap is requested.

estimator="population" explicitly selects the alternative random-design estimator. Its targets at retained N are lambda_star=(N-1)*Var(S)/T, lambda_h=(N-1)*Var(Pi_H S)/T and kappa=Var(Pi_H S)/Var(S), where Pi_H is the linear population projection. Its raw components are V_S=var(Y_mean)-T_mean and V_H=var(Y_mean)-RSS/(N-1-p). This correction assumes a linear conditional mean and homogeneous residual variance. It is different from the manuscript fixed-design correction when uncaptured stable signal remains. Set S_hat=max(0,V_S), H_hat=min(S_hat,max(0,V_H)); estimates multiply these components by (N-1)/T. A non-null model requires positive residual df. population stores these components and estimates only when explicitly selected. This option currently supports intercept adjustment and case resampling; additional nuisance or cluster combinations are rejected explicitly.

With population inference and fixed case strata, variance uses observed proportions w_g, sample variances s_g^2 and means m_g: ⁠sum w_g [1-(1-w_g)/n_g] s_g^2 + sum w_g (m_g-sum w_g m_g)^2⁠. Each such stratum needs two persons. Paper estimation uses projected energies; specifying resampling strata does not change its point estimator.

Ordinary case bootstrap draws N persons with replacement; all measurements, predictors and nuisance variables travel together. Optional strata retain observed case counts. Cluster bootstrap draws the observed number of whole clusters within each stratum; sample size can vary. Cluster labels are scoped within strata. Nuisance effects are refitted on each draw and d is recomputed. Cluster names and strata are sorted for reproducible sampling; case-stratum ordering follows first occurrence. Complete-case selection is shared by all models and precedes sampling. Factor coding is held fixed.

Every draw uses the selected point estimator, including its constraints. Kappa is computed inside each draw. Direct equal-tail percentiles form intervals for T and lambda/kappa. percentile_interpolation="boot" uses boot::boot.ci(type="perc") and normal-quantile interpolation; "type7" uses stats::quantile(type=7), reproducing the manuscript's interpolation. These choices change interpolation only, never the estimator or resampling design. A constant distribution returns identical endpoints. Quantile messages are retained; unavailable quantiles produce NA with quantile_unavailable. Changing confidence level reuses stored draws.

Zero lambda_star is a valid value in its own distribution. With zero estimated total signal, kappa is undefined and stored as NA with reason undefined_kappa. At positive signal, kappa=0 and kappa=1 are valid observations. Original T=0 is singular and skips inference. A resampled T=0 remains a temperature value; the dependent lambda/kappa values in that draw are undefined.

Invalid draws are counted per parameter with reasons; none are replaced. A nonfinite original estimate yields status undefined_estimate. Otherwise, any undefined kappa draw yields undefined_draws; other invalid draws yield failed_draws. The affected regular interval has NA limits. Other parameters retain their own intervals. min_valid applies to quantile calculation. Optional conditional_quantiles=TRUE returns quantiles of finite draws in a separate conditional_quantiles table; these are conditional descriptive quantiles, not regular confidence intervals. n_undefined counts zero-signal kappa draws; n_failed counts all nonfinite parameter values.

Stored draws contain actual parameter estimates including zeros and NA. Optional original row indices and draw_reasons make each draw inspectable. Factor coding is fixed; lost levels and rank loss have explicit diagnostics. Data-dependent formula transforms are rebuilt; formulas must be deterministic. The caller's RNG kind and state are restored. Intervals are pointwise; F_H and delta_F remain point estimates. Interval availability, width and coverage are distinct properties; kappa coverage has no defined target at true zero signal. A runnable regular/weak-signal example is available at system.file("examples", "intervals_and_targets.R", package="lambdastar"). Source that file and call lambdastar_intervals_example(); its retained synthetic datasets have known population targets, while the estimator receives only the observed measurement and predictor columns. The installed doc/MODEL_SPACE_WORKFLOW.md explains why a fixed-profile projection, a finite-N population target and the expectation of the paper statistic differ.

Fixed-reference designs from lambda_reference() use the same paper statistic on departures from a known origin, without an implicit intercept. With no nuisance, d=N and ~1 retains the mean direction. Reference values are subset with the original persons on every draw. lambda_paired() forms matching after-before item differences before estimating T; its T_q is supplied on the mean-difference scale. This path does not extend estimator="population". The derivation is installed as doc/REFERENCE_MEANS.md.

References

https://stat.ethz.ch/R-manual/R-devel/library/boot/html/boot.html https://stat.ethz.ch/R-manual/R-devel/library/boot/html/boot.ci.html

See Also

lambda_bootstrap_control(), confint.lambda_measurement()

Encode contrasts of explicitly specified predictor settings

Description

The grid lists predictor settings; each weights row is a signed contrast over those grid rows and must sum to zero. Supply all averaging weights explicitly (for example -0.5,-0.5,0.5,0.5 for an equally averaged difference). No covariate values, reference population or equal-cell averaging is inferred. The learned polynomial/spline/scale prediction recipe is used to encode the grid in the full model's coordinates, separately in each bootstrap draw. Unsupported sample-dependent transforms require an explicit coefficient L.

Usage

lambda_marginal_contrast(
  data,
  model,
  grid,
  weights,
  contrasts = NULL,
  nuisance = NULL,
  nuisance_contrasts = NULL,
  encoding = c("reevaluate", "fixed")
)

Arguments

Value

A lambda_design as for lambda_contrast(), with grid and weights in its hypothesis metadata. The realized coefficient L is stored on results.

Examples

d <- data.frame(g=factor(rep(c("a","b"),10)), x=seq_len(20))
grid <- data.frame(g=c("a","b"), x=c(10,10), row.names=c("a10","b10"))
lambda_marginal_contrast(d, ~g*x, grid, c(a10=-1,b10=1))

Prepare parallel measurements from a common data frame

Description

Only complete, already scored parallel measurements are supported. Missing cases are rejected by default. Complete-case selection uses whole persons, never a different number of items per person. Point estimates and bootstrap draws use the same explicitly selected estimator.

Usage

lambda_measure(
  data,
  indicators = NULL,
  measurement_scale = c("mean", "item"),
  na.action = c("fail", "complete"),
  bootstrap = FALSE,
  estimator = c("paper", "population"),
  nuisance = NULL,
  nuisance_contrasts = NULL,
  numerical_control = lambda_control(),
  reference = NULL
)

Arguments

Value

A lambda_measurement containing the core measurement state plus included/excluded input positions, original row IDs and effective settings. estimates, inference and settings identify the selected estimator. The paper estimates remain in paper; population is present only when selected.

Evaluate a complete linear hypothesis model

Description

Models describe the hypothesis space after adjustment for the common nuisance design, if supplied separately. Intercepts are removed from the encoded design before ordinary centering. Use ~ 1 for the centered null model. Redundant directions (including a full dummy block from ~ 0 + factor) are rejected, not recoded. A lambda_design(), lambda_hypothesis(), lambda_contrast() or lambda_marginal_contrast() object carries its own coding and nuisance recipe. Non-NULL call settings must agree with the object. A lambda_reference() design instead retains its known origin and explicit mean direction: ~1 is the mean model, ~0 its fixed null. No nuisance intercept is then added implicitly. Reference values travel with rows during resampling. A lambda_panel() design declares person-by-occasion rows with parallel indicators, person-level complete-case selection and whole-person bootstrap. Its default person adjustment uses within-person demeaning; bootstrap copies receive distinct identities. See lambda_panel for the measurement assumptions. Conditional blocks report total structure and kappa after that adjustment. The manuscript path assumes homogeneous isotropic measurement fluctuation, not Gaussian responses or equal total group variances.

Usage

lambda_model(
  data,
  model,
  indicators,
  T_q,
  measurement_scale = c("mean", "item"),
  na.action = c("fail", "complete"),
  contrasts = NULL,
  capacity = c("numerical", "smooth"),
  numerical_control = lambda_control(),
  eta_lookup = NULL,
  response_tol = sqrt(.Machine$double.eps),
  bootstrap = FALSE,
  estimator = c("paper", "population"),
  nuisance = NULL,
  nuisance_contrasts = NULL
)

Arguments

Details

One-sided formulas use the item mean as response. A two-sided formula or lm must have a numeric response equal to that mean on the selected rows. Formula variables must be columns of data. Transformations are evaluated after common case selection; transformation-created missing or infinite values are errors. Factors retain their levels. The actual model.matrix coding determines volume.

Only unweighted, univariate lm objects with an intercept, saved model frame, no offset, and exactly the selected rows in the same order are accepted. The saved response and model matrix are checked against data. The stored contrasts are retained. Objects fitted on different cases must be refitted explicitly. An explicit matrix supplies encoded directions without an intercept, in data row order; when it has row names they must match data before case selection.

F_H always uses the composite mean and its temperature, including when measurement_scale = "item" changes the noncentrality denominator. T_q must therefore be supplied on the composite-mean response scale. Zero temperature returns singular_temperature and NA estimates/F_H, never a boundary estimate.

Value

A lambda_model with raw/constrained noncentralities, basis, case provenance, model metadata (formula, columns, term assignment, contrasts, factor levels, rank), and parsimony containing RSS, costs, volume and F_H.

Examples

set.seed(17)
d <- data.frame(x = rnorm(40), group = factor(rep(c("a", "b"), 20)))
d$i1 <- d$x + rnorm(40)
d$i2 <- d$x + rnorm(40)
lambda_model(d, ~ group + x, c("i1", "i2"), T_q = 1/12)

Evaluate paired mean differences from parallel measurement pairs

Description

Forms after-before within each person and each matching replicate pair, then calls lambda_model with a lambda_reference design. Temperature is estimated from the difference items, retaining homogeneous within-pair error covariance. Different replicate-pair errors must be independent. Persons and both occasions travel together in case or cluster resampling.

Usage

lambda_paired(
  data,
  before,
  after,
  T_q,
  value = 0,
  model = ~1,
  nuisance = NULL,
  contrasts = NULL,
  nuisance_contrasts = NULL,
  encoding = c("reevaluate", "fixed"),
  ...
)

Arguments

Value

A lambda_model plus paired metadata: column pairs, after-minus-before coefficients and the difference matrix in original input-row order. The default ~1 estimates captured mean departure from value. T=0 is singular.

Encode fixed models on person-by-occasion observations

Description

Each row is one person-occasion observation and indicators are parallel measurements within that row. Occasions are not treated as parallel repeats of an unchanged response. The measurement bath must be homogeneous and isotropic across the retained observation space, with independent parallel replicate errors. Person bootstrap does not correct serial measurement error.

Usage

lambda_panel(
  data,
  model = NULL,
  person,
  occasion,
  target = NULL,
  adjust = character(),
  person_effects = c("adjust", "none"),
  contrasts = NULL,
  nuisance = NULL,
  nuisance_contrasts = NULL,
  encoding = c("reevaluate", "fixed")
)

Arguments

Details

Person intercepts are adjusted by default, using group demeaning without a dense dummy matrix. Additional nuisance columns are adjusted in that space. Set person_effects="none" to encode person effects explicitly in model. The person column is treated as a categorical identity, including numeric IDs. Formula columns involving person are rebuilt for distinct sampled copies; fixed encoding of such formulas is rejected. Other fixed bases keep their declared encoding. Explicit matrices encode row-bound non-person directions.

With bootstrap=TRUE in lambda_model/lambda_compare, whole persons are sampled with replacement. An explicit bootstrap control must request cluster resampling with cluster=person. Strata must be constant within persons. Duplicate sampled persons receive distinct draw-level identities. Unbalanced observation counts are allowed, so the number of observation rows and retained df can vary. na.action="complete" excludes an entire person if any required row is incomplete. At least two persons, each with at least two observed occasions, are required.

The default paper estimator, numerical F_H and percentile rules are retained. This does not extend the optional population estimator. Comparisons require the same observation map, person adjustment and nuisance specification.

Value

A row-bound lambda_design with a panel observation map. Evaluation returns panel metadata; retained bootstrap indices also have person_instances giving each sampled copy's draw-local ID in matching row order.

Examples

d <- data.frame(id=rep(1:12,each=3), time=rep(0:2,12))
lambda_panel(d, person="id", occasion="time")
lambda_panel(d, ~time, person="id", occasion="time")
lambda_panel(d, ~id*time, person="id", occasion="time",
  target="id:time", adjust="time")

Encode a hypothesis relative to a known reference

Description

The mean direction is retained: ~1 is a free mean and ~0 is the fixed null value. This extends the centered manuscript calculation to a prespecified affine origin. Formula intercepts are retained, including in an explicitly supplied nuisance formula; use ~0+x for nuisance x without an intercept. Reference values must be known independently of this analysis.

Usage

lambda_reference(
  data,
  model = ~1,
  value = 0,
  nuisance = NULL,
  contrasts = NULL,
  nuisance_contrasts = NULL,
  encoding = c("reevaluate", "fixed")
)

Arguments

Details

All compared models must declare the same reference and nuisance recipe. The ordinary centered API is unchanged. This path uses estimator="paper"; it does not extend the population estimator or the centered L beta=0 helpers. See the installed derivation at system.file("doc","REFERENCE_MEANS.md",package="lambdastar").

Value

A row-bound lambda_design with an explicit fixed reference. After evaluation, reference, mean_departure and retained df describe the origin and signed mean departure after any nuisance adjustment. Lambda values quantify squared departures; F_H uses the uncentered adjusted coding.

Examples

d <- data.frame(x=seq_len(20))
lambda_reference(d, ~1, value=50)
lambda_reference(d, ~0, value=50)

Build a reusable capacity integral lookup

Description

An adaptively refined mesh approximates eta by linear segments. Their integrals are accumulated and evaluated quadratically inside each segment. Below min_ratio, direct quadrature is used, preventing extrapolation of the first interval into the singular boundary region. Local trapezoidal errors are estimated by refinement; these estimates are not rigorous bounds.

Usage

make_eta_numerical_lookup(
  max_ratio,
  min_ratio = max_ratio * 1e-06,
  grid_points = 65L,
  control = lambda_control()
)

Arguments

Value

An eta_numerical_lookup object with nodes, capacities, cumulative integrals, estimated errors, and its actual numerical controls.

Inspect Lambda Star results

Description

Inspect Lambda Star results

Usage

## S3 method for class 'lambda_ci'
print(x, digits = max(3L, getOption("digits") - 3L), ...)

## S3 method for class 'lambda_measurement'
summary(object, ...)

## S3 method for class 'lambda_model'
summary(object, ...)

## S3 method for class 'lambda_comparison'
summary(object, ...)

## S3 method for class 'lambda_measurement'
print(x, digits = max(3L, getOption("digits") - 3L), ...)

## S3 method for class 'lambda_model'
print(x, digits = max(3L, getOption("digits") - 3L), ...)

## S3 method for class 'lambda_comparison'
print(x, digits = max(3L, getOption("digits") - 3L), ...)

## S3 method for class 'lambda_summary'
print(x, digits = max(3L, getOption("digits") - 3L), ...)

## S3 method for class 'lambda_comparison_summary'
print(x, digits = max(3L, getOption("digits") - 3L), ...)

Arguments

Value

Summary methods return inspectable summary lists. Print methods return their input invisibly. Full encoded matrices remain in the original results.

Project a vector using an orthonormal basis

Description

Project a vector using an orthonormal basis

Usage

project_onto_basis(x, q)

Arguments

Value

Numeric projected vector. No N by N projector is constructed.

Evaluate the parsimony functional for one encoded hypothesis

Description

The response and supplied temperature must describe the same measurement representation. For a mean of parallel items use its composite_mean temperature, not the single-item temperature. The encoded X determines volume; its orthonormal basis is used only for projection.

Usage

thermodynamic_model_state(
  response,
  x,
  temperature,
  resolution,
  model = "H",
  control = lambda_control(),
  eta_method = c("numerical", "smooth"),
  eta_lookup = NULL,
  boundary = FALSE,
  nuisance = NULL,
  reference = NULL
)

Arguments

Value

List containing status, model, n, df_h, df_perp, rss, log_volume, volume, temperature, resolution, xi_eta, xi_a, dimension_cost, geometry_cost, free_energy, numerical diagnostics and encoded basis. At T=0 regular estimation returns NA for the thermal terms and F_H. boundary=TRUE instead labels the result boundary_only; it is not inference.

Integrate numerical capacity over temperature

Description

Integrate numerical capacity over temperature

Usage

xi_eta_numerical(
  temperature,
  resolution,
  lookup = NULL,
  control = lambda_control(),
  details = FALSE
)

Arguments

Value

Numeric integral values, or a list containing value, abs_error, method and control. Lookup error estimates describe mesh discretization; solver/truncation tolerances are recorded separately in control.