Diagnose and Remedy Model Assumptions

agriDesignR contributors

library(agriDesignR)
data("tomato_rcbd", package = "agriDesignR")

Check design and response data

The tomato data contain an RCBD with an intentionally incomplete or unbalanced layout and a plant-density covariate. check_design() reports missingness, cell counts, blocking, and response characteristics before model fitting.

design <- check_design(
  data = tomato_rcbd,
  response = "fruit_weight",
  treatment = "treatment",
  block = "block",
  covariates = "plant_density"
)

design$balance_status
#> [1] "balanced"
design$response_audit
#> $n_total
#> [1] 20
#> 
#> $n_observed
#> [1] 18
#> 
#> $n_unique
#> [1] 18
#> 
#> $n_na
#> [1] 2
#> 
#> $pct_na
#> [1] 10
#> 
#> $is_numeric
#> [1] TRUE
#> 
#> $is_integer_like
#> [1] FALSE
#> 
#> $has_negatives
#> [1] FALSE
#> 
#> $has_zeros
#> [1] FALSE
#> 
#> $pct_zeros
#> [1] 0
#> 
#> $is_proportion
#> [1] FALSE
#> 
#> $has_proportion_boundary
#> [1] FALSE
#> 
#> $is_percentage
#> [1] FALSE
#> 
#> $is_binary
#> [1] FALSE
#> 
#> $max_value
#> [1] 135.68
#> 
#> $min_value
#> [1] 93.86
#> 
#> $skewness
#> [1] -0.07780486
#> 
#> $suggested_family
#> [1] "gaussian (standard normal linear model)"
design$warnings
#> character(0)

Fit and inspect assumptions

Use the fixed-effects engine here to show a classical RCBD analysis with the covariate. In a real study, choose fixed versus random block effects from the sampling and randomization plan, not from a p-value.

fit <- fit_experiment(
  data = tomato_rcbd,
  response = "fruit_weight",
  treatment = "treatment",
  block = "block",
  covariates = "plant_density",
  engine = "lm"
)

fit$assumptions$overall_status
#> [1] "ACCEPTABLE_WITH_CAUTIONS"
fit$assumptions$normality$message
#> [1] "Mild deviation from normality (W = 0.861, p = 0.0128, skewness = 0.93). ANOVA F-tests remain robust under moderate sample sizes."
fit$assumptions$homoscedasticity$message
#> [1] "Equal variance across treatment groups confirmed (Variance ratio max/min = 2.37x, Levene p = 0.996)."

The audit is a screening aid. Residual plots, study-specific knowledge, and the consequences for the estimand remain necessary before changing model.

with(fit, {
  graphics::plot(
    stats::fitted(model),
    stats::residuals(model),
    xlab = "Fitted values",
    ylab = "Residuals"
  )
  graphics::abline(h = 0, lty = 2, col = "grey40")
})

Evaluate a transformation as sensitivity analysis

remedy() can fit a transformed response or a heterogeneous-variance model. The automatic option is inspectable: compare returned fits, assumptions, and scientific interpretation before selecting a final analysis.

boxcox_fit <- remedy(fit, method = "boxcox")
boxcox_fit$remedy_type
#> [1] "Log Transformation (ln(y))"
boxcox_fit$comparison_table
#>                           Metric                           Original_Model
#> 1                  Model Formula fruit_weight ~ treatment + plant_density
#> 2                Engine / Family                          base (gaussian)
#> 3                            AIC                                   124.62
#> 4                            BIC                                   129.96
#> 5 Residual Normality (Shapiro p)                                   0.0128
#> 6       Variance Ratio (max/min)                                     2.37
#> 7          Overall Health Status                 ACCEPTABLE_WITH_CAUTIONS
#>                                   Remedied_Model
#> 1 fruit_weight_trans ~ treatment + plant_density
#> 2                                base (gaussian)
#> 3                                         -45.85
#> 4                                         -40.51
#> 5                                         0.0203
#> 6                                           2.97
#> 7                       ACCEPTABLE_WITH_CAUTIONS
boxcox_fit$verdict
#> [1] "[OK] REMEDY SUBSTANTIALLY IMPROVED: Residual metrics improved significantly and are now well within acceptable limits for robust inference."

For count responses, consider a Poisson or negative-binomial model rather than transforming counts solely to satisfy Gaussian residual diagnostics. For repeated measurements, model within-subject dependence explicitly. Do not use a remedy to hide flawed randomization or turn a post-hoc choice into a confirmatory claim.