Introduction to modeldiag
Overview
Statistical models rely on assumptions for valid inference. Violations of these assumptions can lead to biased estimates, incorrect standard errors, and misleading conclusions.
The modeldiag package provides a unified framework for
diagnosing these assumptions across multiple model classes,
including:
- Linear models
- Logistic regression
- Count models (Poisson)
- Survival models (Cox proportional hazards)
This vignette introduces both the statistical
intuition behind common diagnostics and how to implement them
using modeldiag.
Linear Models
Consider the classical linear regression model:
\[Y = X\beta + \varepsilon, \quad \varepsilon \sim N(0, \sigma^2 I)\]
Valid inference depends on several assumptions about the error term \(\varepsilon\).
Multicollinearity
Multicollinearity occurs when predictors are highly correlated. This inflates the variance of coefficient estimates.
The Variance Inflation Factor (VIF) is defined as:
\[\text{VIF}_j = \frac{1}{1 - R_j^2}\]
where \(R_j^2\) is obtained by regressing predictor \(X_j\) on all other predictors.
Large VIF values indicate unstable estimates.
Heteroscedasticity
Heteroscedasticity occurs when:
\[ \text{Var}(\varepsilon_i) \neq \sigma^2 \]
The Breusch–Pagan test evaluates whether residual variance depends on predictors.
Autocorrelation
Autocorrelation arises when:
\[\text{Cov}(\varepsilon_i, \varepsilon_j) \neq 0\]
The Durbin–Watson statistic tests for first-order autocorrelation.
Normality of Errors
Many inferential procedures assume:
\[ \varepsilon \sim N(0, \sigma^2) \]
The Shapiro–Wilk test evaluates this assumption.
Influential Observations
Influential points disproportionately affect model estimates. Cook’s distance measures this influence:
\[ D_i = \frac{( \hat{\beta} - \hat{\beta}*{(i)} )^T X^T X (\hat{\beta} - \hat{\beta}*{(i)})}{p \hat{\sigma}^2} \]
Example
model_lm <- lm(mpg ~ wt + hp + disp, data = mtcars)
diag_lm <- diagnose_model(model_lm)
summary(diag_lm)
#> -- Model Diagnostics Summary ---------------------------------------------------
#>
#> -- multicollinearity --
#>
#> -- Variance inflation factors
#>
#> wt hp disp
#> 4.844618 2.736633 7.324517
#> -- VIF severity by predictor:
#>
#> wt hp disp
#> "Moderate" "Moderate" "High"
#> -- Severity legend:
#> * < 2 : Negligible
#> * 2 - 5 : Moderate
#> * 5 - 10 : High
#> * >= 10 : Severe
#>
#> -- heteroskedasticity --
#>
#> p-value: 0.8143398
#> Residual variance appears approximately constant.
#>
#> -- autocorrelation --
#>
#> p-value: 0.01611772
#> Residuals appear autocorrelated; consider time-series adjustments.
#>
#> -- linearity --
#>
#> p-value: 0.000869965
#> Evidence against linearity in the model; consider adding nonlinear terms or transformations.
#>
#> -- normality --
#>
#> p-value: 0.03304597
#> Residuals deviate from normality; check model assumptions.
#>
#> -- outliers --
#>
#> Number of influential points: 3
#> Influential observations: Chrysler Imperial, Toyota Corolla, Maserati Bora
#> Cook's distances for influential observations:
#> Chrysler Imperial Toyota Corolla Maserati Bora
#> 0.3199707 0.1529771 0.3402911
#> 3 influential observation(s) detected. Influential observations have Cook's distance above 4/n. Review these cases for leverage, data entry issues, or model fit problems.You can also run individual checks when you only need one diagnostic.
check_vif(model_lm)
#> $success
#> [1] TRUE
#>
#> $vif
#> wt hp disp
#> 4.844618 2.736633 7.324517
#>
#> $note
#> [1] "VIF severity by predictor: wt (Moderate), hp (Moderate), disp (High)"
#>
#> $collinear_predictors
#> character(0)
#>
#> $severities
#> wt hp disp
#> "Moderate" "Moderate" "High"
check_heteroskedasticity(model_lm)
#>
#> studentized Breusch-Pagan test
#>
#> data: model
#> BP = 0.9459, df = 3, p-value = 0.8143
check_autocorrelation(model_lm)
#>
#> Durbin-Watson test
#>
#> data: model
#> DW = 1.3673, p-value = 0.01612
#> alternative hypothesis: true autocorrelation is greater than 0
check_linearity(model_lm)
#>
#> RESET test
#>
#> data: model
#> RESET = 14.01, df1 = 1, df2 = 27, p-value = 0.00087
check_normality(model_lm)
#>
#> Shapiro-Wilk normality test
#>
#> data: res
#> W = 0.92734, p-value = 0.03305
check_outliers(model_lm)
#> $cooks_distance
#> Mazda RX4 Mazda RX4 Wag Datsun 710 Hornet 4 Drive
#> 1.152035e-02 4.621112e-03 1.598334e-02 1.283888e-04
#> Hornet Sportabout Valiant Duster 360 Merc 240D
#> 1.839055e-03 1.560119e-02 1.053270e-02 1.313511e-02
#> Merc 230 Merc 280 Merc 280C Merc 450SE
#> 2.525382e-03 3.671067e-03 2.606104e-02 1.551454e-03
#> Merc 450SL Merc 450SLC Cadillac Fleetwood Lincoln Continental
#> 1.049983e-04 5.648180e-03 7.218880e-05 1.298764e-02
#> Chrysler Imperial Fiat 128 Honda Civic Toyota Corolla
#> 3.199707e-01 1.196019e-01 9.092102e-03 1.529771e-01
#> Toyota Corona Dodge Challenger AMC Javelin Camaro Z28
#> 2.215865e-02 4.218196e-02 4.909944e-02 7.181085e-03
#> Pontiac Firebird Fiat X1-9 Porsche 914-2 Lotus Europa
#> 6.980693e-02 4.163138e-04 1.732523e-06 5.959750e-02
#> Ford Pantera L Ferrari Dino Maserati Bora Volvo 142E
#> 7.279943e-03 1.100867e-02 3.402911e-01 8.796726e-03
#>
#> $influential_points
#> Chrysler Imperial Toyota Corolla Maserati Bora
#> 17 20 31Logistic Regression
Logistic regression models the probability:
\[ \text{logit}(P(Y=1)) = X\beta \]
Key Diagnostics
Linearity of the Logit
The model assumes a linear relationship between predictors and the log-odds:
\[ \log\left(\frac{p}{1-p}\right) \]
The Box–Tidwell test evaluates this assumption.
Goodness of Fit
The Hosmer–Lemeshow test compares observed and expected counts across groups.
Separation
Complete or quasi-complete separation occurs when predictors perfectly classify outcomes, leading to unstable or infinite estimates.
Example
model_glm <- glm(am ~ wt + hp, data = mtcars, family = binomial)
diag_glm <- diagnose_model(model_glm)
summary(diag_glm)
#> -- Model Diagnostics Summary ---------------------------------------------------
#>
#> -- multicollinearity --
#>
#> -- Variance inflation factors
#>
#> wt hp
#> 2.444297 2.444297
#> -- VIF severity by predictor:
#>
#> wt hp
#> "Moderate" "Moderate"
#> -- Severity legend:
#> * < 2 : Negligible
#> * 2 - 5 : Moderate
#> * 5 - 10 : High
#> * >= 10 : Severe
#>
#> -- linearity_logit --
#>
#> MLE of lambda Score Statistic (t) Pr(>|t|)
#> wt -0.088743 2.2318 0.03412 *
#> hp 3.205811 0.8980 0.37711
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> iterations = 13
#>
#> Score test for null hypothesis that all lambdas = 1:
#> F = 3.6654, df = 2 and 27, Pr(>F) = 0.03905
#>
#>
#> -- goodness_of_fit --
#>
#> p-value: 0.6716511
#> Model fit appears adequate.
#>
#> -- influential_observations --
#>
#> Number of influential points: 2
#> Influential observations: Mazda RX4 Wag, Toyota Corona
#> Cook's distances for influential observations:
#> Mazda RX4 Wag Toyota Corona
#> 0.2034041 0.7917908
#> 2 influential observation(s) detected. Influential observations have Cook's distance above 4/n. Review these cases for leverage, data entry issues, or model fit problems.
#>
#> -- separation_issues --
#>
#> No separation issues detected.Individual logistic regression diagnostics can be called directly.
check_box_tidwell(model_glm)
#> MLE of lambda Score Statistic (t) Pr(>|t|)
#> wt -0.088743 2.2318 0.03412 *
#> hp 3.205811 0.8980 0.37711
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> iterations = 13
#>
#> Score test for null hypothesis that all lambdas = 1:
#> F = 3.6654, df = 2 and 27, Pr(>F) = 0.03905
check_hosmer_lemeshow(model_glm)
#>
#> Hosmer and Lemeshow goodness of fit (GOF) test
#>
#> data: model$y, fitted(model)
#> X-squared = 2.3502, df = 4, p-value = 0.6717
check_influential_glm(model_glm)
#> $cooks_distance
#> Mazda RX4 Mazda RX4 Wag Datsun 710 Hornet 4 Drive
#> 1.725110e-02 2.034041e-01 1.054039e-03 1.686756e-03
#> Hornet Sportabout Valiant Duster 360 Merc 240D
#> 3.512351e-03 4.413520e-05 9.441132e-02 1.553660e-04
#> Merc 230 Merc 280 Merc 280C Merc 450SE
#> 1.805692e-03 1.692468e-04 1.692468e-04 9.043823e-07
#> Merc 450SL Merc 450SLC Cadillac Fleetwood Lincoln Continental
#> 1.047495e-04 5.277112e-05 1.234078e-13 1.734386e-14
#> Chrysler Imperial Fiat 128 Honda Civic Toyota Corolla
#> 1.619112e-13 1.309867e-03 7.429752e-07 7.402953e-06
#> Toyota Corona Dodge Challenger AMC Javelin Camaro Z28
#> 7.917908e-01 2.834875e-04 8.715763e-04 1.812379e-03
#> Pontiac Firebird Fiat X1-9 Porsche 914-2 Lotus Europa
#> 1.563880e-05 2.899997e-05 9.799693e-05 2.790544e-09
#> Ford Pantera L Ferrari Dino Maserati Bora Volvo 142E
#> 5.218144e-03 2.458477e-03 8.109529e-02 1.007256e-01
#>
#> $influential_points
#> Mazda RX4 Wag Toyota Corona
#> 2 21
check_separation(model_glm)
#> [1] "No separation issues detected."Poisson Regression
Poisson regression assumes:
\[ Y \sim \text{Poisson}(\lambda), \quad \log(\lambda) = X\beta \]
Overdispersion
A key assumption is:
\[ \text{Var}(Y) = \mathbb{E}(Y) \]
Overdispersion occurs when:
\[ \text{Var}(Y) > \mathbb{E}(Y) \]
This leads to underestimated standard errors.
Zero Inflation
Excess zeros beyond what the Poisson model predicts may indicate a zero-inflated process.
Example
model_pois <- glm(carb ~ wt + hp, data = mtcars, family = poisson)
diag_pois <- diagnose_model(model_pois)
summary(diag_pois)
#> -- Model Diagnostics Summary ---------------------------------------------------
#>
#> -- multicollinearity --
#>
#> -- Variance inflation factors
#>
#> wt hp
#> 1.401553 1.401553
#> -- VIF severity by predictor:
#>
#> wt hp
#> "Negligible" "Negligible"
#> -- Severity legend:
#> * < 2 : Negligible
#> * 2 - 5 : Moderate
#> * 5 - 10 : High
#> * >= 10 : Severe
#>
#> -- overdispersion --
#>
#> Residual deviance: 12.27804
#> Degrees of freedom: 29
#> Ratio: 0.4233806
#> [OK] No evidence of overdispersion.
#>
#> -- zero_inflation --
#>
#> Observed zeros: 0 ( 0 %)
#> Expected zeros: 3 ( 9.3 %)
#> [OK] No evidence of zero-inflation.
#>
#> -- influential_observations --
#>
#> Number of influential points: 0
#> No observations exceed the influence threshold.
#> No influential observations detected. Influential observations have Cook's distance above 4/n. Review these cases for leverage, data entry issues, or model fit problems.
#>
#> -- residual_analysis --
#>
#> Mean residual: -0.04200633
#> SD residual: 0.6278888
#> Min residual: -0.8656074
#> Max residual: 1.497036Individual Poisson diagnostics are available for targeted checks.
check_overdispersion(model_pois)
#> $residual_deviance
#> [1] 12.27804
#>
#> $df
#> [1] 29
#>
#> $ratio
#> [1] 0.4233806
#>
#> $overdispersed
#> [1] FALSE
check_zero_inflation(model_pois)
#> $observed_zeros
#> [1] 0
#>
#> $expected_zeros
#> [1] 2.978489
#>
#> $prop_observed
#> [1] 0
#>
#> $prop_expected
#> [1] 0.09307777
#>
#> $zero_inflated
#> [1] FALSE
check_residual_analysis(model_pois)
#> $mean_residual
#> [1] -0.04200633
#>
#> $sd_residual
#> [1] 0.6278888
#>
#> $min_residual
#> [1] -0.8656074
#>
#> $max_residual
#> [1] 1.497036Survival Models
The Cox proportional hazards model assumes:
\[ h(t | X) = h_0(t) \exp(X\beta) \]
Proportional Hazards
The key assumption is that hazard ratios are constant over time.
Schoenfeld residuals are used to test:
\[ \frac{\partial \beta(t)}{\partial t} = 0 \]
Example
library(survival)
data(lung)
#> Warning in data(lung): data set 'lung' not found
model_cox <- coxph(Surv(time, status) ~ age + sex + ph.ecog, data = lung)
diag_cox <- diagnose_model(model_cox)
summary(diag_cox)
#> -- Model Diagnostics Summary ---------------------------------------------------
#>
#> -- multicollinearity --
#>
#> VIF not applicable to Cox models (no intercept).
#>
#> -- proportional_hazards --
#>
#> Global test p-value: 0.2155549
#> chisq df p
#> age 0.1879877 1 0.6645968
#> sex 2.3054372 1 0.1289220
#> ph.ecog 2.0542488 1 0.1517821
#> GLOBAL 4.4636576 3 0.2155549
#> Proportional hazards assumption appears reasonable.
#>
#> -- influential_observations --
#>
#> Number of influential points: 10
#> Influential observations: 3, 6, 17, 32, 36, 37, 70, 84, 88, 128
#> Max |dfbeta| for influential observations:
#> 3 6 18 33 37 38 71 85
#> 0.2103167 0.4334764 0.3724475 0.2236608 0.5149764 0.2628997 0.2410623 0.4614677
#> 89 129
#> 0.2431150 0.2057780
#> Influential observations have |dfbeta| > 0.2 for at least one coefficient. Review these cases.
#>
#> -- functional_form --
#>
#> Functional form check: Review plots of martingale residuals vs predictors for nonlinearity.Individual Cox model diagnostics can also be run directly.
check_proportional_hazards(model_cox)
#> chisq df p
#> age 0.188 1 0.66
#> sex 2.305 1 0.13
#> ph.ecog 2.054 1 0.15
#> GLOBAL 4.464 3 0.22
check_influential_coxph(model_cox)
#> $dfbetas
#> [,1] [,2] [,3]
#> 1 0.0019898612 -0.0113782893 6.631006e-03
#> 2 0.0083884583 -0.0044437262 -6.509521e-03
#> 3 0.1035755702 0.1037120879 2.103167e-01
#> 4 -0.0330380008 -0.0286728004 9.415764e-03
#> 5 -0.0205151822 0.0770639215 1.786017e-01
#> 6 -0.4334763687 0.2231627194 4.290399e-02
#> 7 0.0034484450 0.0074885523 2.217729e-02
#> 8 -0.0034354243 -0.0123156330 -1.720884e-03
#> 9 -0.0545859489 -0.0290902376 1.532795e-02
#> 10 -0.0203524286 -0.0299237994 6.005745e-02
#> 11 -0.0402721682 -0.0359013581 6.946416e-03
#> 12 -0.0204388391 -0.1328570080 -1.186494e-01
#> 13 -0.0269608241 -0.0845550087 2.599462e-02
#> 15 0.0500749523 0.0468657714 3.676696e-03
#> 16 0.0255499998 -0.0378692577 -8.237601e-03
#> 17 -0.0673005764 0.0666616602 1.859480e-02
#> 18 0.0677805147 0.2071896397 -3.724475e-01
#> 19 -0.0767254887 0.1041755665 9.100104e-02
#> 20 -0.0490731482 -0.0420620976 -5.505968e-03
#> 21 0.0040113166 -0.0156559500 7.076112e-03
#> 22 -0.1052516339 0.1201631714 -1.113843e-01
#> 23 0.1109014162 0.0419282449 -1.271730e-02
#> 24 -0.0065294229 -0.0179439992 -2.854969e-02
#> 25 0.0100368581 -0.0092537857 -1.174584e-02
#> 26 0.0074129218 -0.0058340366 -9.803345e-04
#> 27 0.0059441198 0.0102630835 2.902271e-02
#> 28 0.0124397186 -0.0267581202 9.171121e-02
#> 29 0.0059686416 0.0035966310 5.447686e-03
#> 30 0.0737321000 -0.0475682053 7.247954e-02
#> 31 0.0083865691 -0.0011721621 -4.563597e-03
#> 32 0.0643205077 -0.0470553678 7.190084e-02
#> 33 0.2236608432 0.0820904131 -1.761672e-01
#> 34 -0.0395963375 0.0956478074 8.223422e-02
#> 35 -0.0348741914 -0.0476125800 8.855613e-02
#> 36 -0.0220042339 0.0908613070 8.036788e-02
#> 37 -0.0273847520 0.2983457171 -5.149764e-01
#> 38 -0.0610066728 -0.2628997035 1.205452e-02
#> 39 0.0581492118 -0.0388606066 5.839455e-02
#> 40 0.0019819640 -0.0765191629 2.040386e-02
#> 41 -0.0346977518 0.0282497267 5.503139e-03
#> 42 0.0504437379 0.0799540315 6.056346e-02
#> 43 -0.0109086809 0.0571036938 -6.101022e-02
#> 44 -0.0378742791 0.0851494384 8.073107e-02
#> 45 -0.0444443723 0.0614457376 1.687138e-02
#> 46 0.0832006255 0.0939766536 5.810064e-02
#> 47 0.0482339850 -0.0284671687 -4.845867e-02
#> 48 0.0098492845 0.0306396494 3.653707e-04
#> 49 -0.0632893286 0.0259644093 8.006261e-02
#> 50 0.0756767437 -0.0407024519 6.631776e-03
#> 51 -0.0681197399 -0.0951568481 3.355310e-02
#> 52 0.0121286330 -0.0378057000 -8.028300e-02
#> 53 0.0622907567 -0.0398198704 -1.336872e-01
#> 54 -0.0228659361 -0.0330608778 -5.927036e-02
#> 55 0.0641758549 0.0836364116 -8.760249e-03
#> 56 0.0098180554 -0.0392584149 -1.201191e-01
#> 57 0.0319091035 0.1291139999 -1.443057e-01
#> 58 -0.0498881164 -0.0369076822 7.852703e-02
#> 59 0.0299205943 -0.0372026229 -1.656423e-04
#> 60 0.0018451697 0.0402453130 1.318178e-03
#> 61 -0.0367924289 -0.0534874473 -3.852699e-02
#> 62 -0.0785338667 -0.0322244907 2.131399e-02
#> 63 0.0535821256 -0.0324735308 -8.568132e-03
#> 64 0.0183300113 0.1130154262 -2.729181e-02
#> 65 0.0352581667 -0.0346338143 -7.358120e-03
#> 66 0.0221439514 -0.0433611232 7.221090e-02
#> 67 0.0045346445 0.0535580295 5.434215e-02
#> 68 -0.0397442023 -0.1522338787 1.527123e-01
#> 69 0.0102568136 -0.0115179178 -1.423718e-02
#> 70 0.0086164345 -0.0255925458 6.027162e-03
#> 71 -0.0470406846 0.1049392189 2.410623e-01
#> 72 -0.0860754948 0.0580683479 1.408366e-02
#> 73 0.0740966086 -0.0479245443 7.394157e-02
#> 74 -0.1758878058 -0.0413044150 2.481401e-02
#> 75 -0.0719470999 0.0762086036 1.173566e-02
#> 76 0.0148082806 0.0176939652 -4.434004e-04
#> 77 -0.0046672396 0.0192137723 -1.813395e-02
#> 78 -0.0266390434 0.0438138804 5.989556e-03
#> 79 0.1782533223 -0.0375607865 -1.604460e-01
#> 80 0.0816850630 -0.0351846583 -9.804956e-02
#> 81 0.0152779990 0.0793079902 1.189438e-01
#> 82 -0.0636198968 -0.0416836601 -1.306606e-03
#> 83 0.0698051012 0.0177935997 -8.281316e-03
#> 84 -0.1503150506 0.0968834915 1.709307e-02
#> 85 0.4614677138 0.1477727601 -8.810651e-02
#> 86 0.0154474340 -0.0164739726 5.604348e-04
#> 87 0.0085719629 -0.0322435760 6.264670e-03
#> 88 -0.0013733406 -0.0371414066 -9.646258e-02
#> 89 0.2431149833 -0.1546166164 -3.292858e-02
#> 90 0.0276317853 -0.0270515449 4.773117e-02
#> 91 0.0045977579 0.0259099959 5.980967e-02
#> 92 0.0177403510 -0.0242814478 4.411387e-03
#> 93 0.0230650286 -0.0412215026 -1.773923e-02
#> 94 -0.0426823226 0.0720064653 7.098509e-03
#> 95 -0.0564521384 -0.0891532850 1.010963e-01
#> 96 0.0559648269 -0.0471252036 7.343045e-02
#> 97 0.0308758962 -0.0326325335 -4.524247e-03
#> 98 0.0032395515 -0.0123927821 6.627081e-03
#> 99 0.0026180610 0.0263848968 -1.344832e-03
#> 100 0.0721113689 0.1060389633 -1.188152e-01
#> 101 0.0177466831 -0.0726996366 7.216985e-02
#> 102 0.0117130597 0.0108225866 -3.319975e-03
#> 103 0.0069108034 -0.0005234452 5.100927e-03
#> 104 -0.0001501724 -0.0393164284 -9.816928e-03
#> 105 -0.0263533710 -0.0274232475 5.503929e-02
#> 106 0.0177062136 -0.0349541815 -5.748319e-03
#> 107 0.0755001113 -0.0979229433 -3.288944e-03
#> 108 0.0304753917 -0.0432099350 -2.589854e-02
#> 109 0.0173499082 0.0059787081 4.846321e-06
#> 110 -0.0058002274 -0.0133607874 4.140821e-04
#> 111 0.0700097729 -0.0389969262 -1.378760e-01
#> 112 -0.1221994328 -0.0383062757 2.203808e-02
#> 113 0.0220568694 -0.0122813838 -4.022791e-05
#> 114 0.0996231959 0.0939974470 -1.118615e-01
#> 115 -0.0012572451 0.0111730974 3.545064e-04
#> 116 0.0908990976 -0.0473912195 6.914276e-02
#> 117 -0.0456730504 -0.0178610689 4.539084e-02
#> 118 -0.0345055675 0.1105009415 -1.877604e-01
#> 119 -0.0013697789 0.0093433174 -2.210654e-02
#> 120 -0.0482933670 0.0149483922 1.588416e-02
#> 121 0.0033460475 -0.0064066864 -2.122262e-03
#> 122 -0.0327622814 0.0595625887 6.736237e-02
#> 123 -0.0070824888 -0.0145286411 1.332550e-02
#> 124 0.0548688520 -0.0463741344 7.072927e-02
#> 125 -0.0152959088 0.0160355428 4.569608e-02
#> 126 0.0086214315 -0.0274821266 1.781469e-03
#> 127 -0.1058282819 -0.0427239316 4.120953e-03
#> 128 0.0088710803 -0.0443495143 -1.725015e-02
#> 129 -0.2057779582 -0.2008082718 -1.535928e-01
#> 130 0.0645107804 -0.0618179518 5.331680e-02
#> 131 -0.0236343483 0.0568749151 5.914936e-03
#> 132 -0.0561439462 -0.0321416892 1.270814e-02
#> 133 -0.0586991589 -0.0274863346 -3.480657e-02
#> 134 0.0630172285 -0.0910178391 -1.778694e-03
#> 135 0.0258463538 -0.0304889411 -6.461534e-02
#> 136 -0.1279169393 -0.1704506884 -1.371350e-01
#> 137 -0.0154086097 0.0390418564 4.024052e-03
#> 138 0.0669074111 0.0465558493 -8.898263e-02
#> 139 0.0351034039 0.0152623303 -7.214797e-03
#> 140 -0.0226985456 -0.0324411456 -3.972187e-02
#> 141 0.0325169319 0.0523084757 4.975478e-02
#> 142 -0.1365688305 0.0766382561 2.797470e-02
#> 143 -0.0064160386 -0.0033925776 1.074984e-02
#> 144 0.0178556896 0.1126558464 -2.672885e-02
#> 145 0.0810398492 0.0771006813 -1.007872e-02
#> 146 0.0521580824 -0.0609825008 -2.466540e-03
#> 147 0.0265819228 -0.0190045447 -3.048193e-02
#> 148 -0.0624588814 -0.0373134387 8.855150e-03
#> 149 0.1854018296 -0.0391263682 -1.543971e-01
#> 150 -0.0146643351 0.0695887941 -7.216112e-02
#> 151 0.0179795901 -0.0245133503 4.575647e-03
#> 152 0.0100768982 0.0424254888 9.334078e-02
#> 153 -0.0021287480 -0.0376693165 3.921463e-02
#> 154 -0.0772132998 0.0877302195 6.475027e-03
#> 155 -0.0559623188 -0.0325046362 7.261258e-02
#> 156 -0.0176598590 0.0235222457 -4.779548e-02
#> 157 -0.0293957133 -0.0773271267 1.311357e-02
#> 158 0.0068052932 0.0062231396 -1.786702e-02
#> 159 -0.0023248131 -0.0339887124 9.058203e-04
#> 160 0.0424716224 -0.0699038077 -1.947040e-04
#> 161 -0.0029328740 -0.0493669420 5.139855e-02
#> 162 -0.1285114884 0.0757464819 1.809179e-02
#> 163 -0.0419861306 0.0756456597 -1.289759e-01
#> 164 -0.0018120797 -0.0384883650 -3.677971e-03
#> 165 -0.0066361460 0.0689299192 5.032142e-03
#> 166 0.0083931592 -0.0261948636 2.556857e-02
#> 167 -0.0242361426 0.0827222971 -1.754309e-03
#> 168 -0.0747706920 -0.0344385691 -4.081238e-02
#> 169 -0.0145645184 -0.0347051334 4.195715e-03
#> 170 0.0176905893 -0.0301505049 -6.129940e-02
#> 171 0.0176428967 0.0412026013 1.648694e-03
#> 172 -0.0207180251 0.0703990895 -7.092345e-02
#> 173 -0.0423107365 -0.0344824534 9.182614e-03
#> 174 0.0573040836 -0.0398398542 3.132242e-02
#> 175 0.0706157052 0.0386845932 -7.955815e-03
#> 176 0.0175625437 -0.0498843953 3.139427e-03
#> 177 -0.0376920672 -0.0274684521 5.621938e-02
#> 178 -0.0600856029 0.0853066677 5.266695e-03
#> 179 -0.0816891797 0.1008438435 1.361401e-03
#> 180 -0.0323883857 -0.0334131872 3.991434e-02
#> 181 0.0057921807 0.0224610020 5.465954e-02
#> 182 0.0704448675 0.0159698178 2.765059e-02
#> 183 0.0267115415 0.0667750050 -7.525088e-02
#> 184 -0.0060728312 -0.0466007828 7.070918e-03
#> 185 0.0232586076 -0.0295436234 2.647552e-02
#> 186 0.0407291304 -0.0321686957 2.626321e-02
#> 187 0.0154698862 0.0239576638 2.675119e-02
#> 188 0.0114213958 0.0173517892 4.243866e-02
#> 189 0.0071288629 -0.0384936423 -1.060828e-02
#> 190 -0.0444176004 -0.0317421508 -5.581723e-02
#> 191 0.0159454594 -0.0165595624 1.085787e-03
#> 192 -0.0993555065 -0.0441102767 9.409598e-02
#> 193 -0.0969346845 -0.0400537973 1.122165e-02
#> 194 -0.0035331076 0.0285724239 5.525394e-03
#> 195 0.0137088532 -0.0175698624 1.987928e-03
#> 196 -0.0309687876 0.0170386947 5.052130e-02
#> 197 0.0010346898 -0.0410911928 5.400080e-03
#> 198 -0.0037269810 0.0355762475 5.400631e-03
#> 199 0.0187209222 -0.0265200538 2.411146e-02
#> 200 -0.0230595855 -0.0389285154 -1.259133e-04
#> 201 0.0094105104 0.1112473351 -2.467330e-02
#> 202 0.0842868100 -0.0438952808 -3.013321e-02
#> 203 -0.0037067535 -0.0270728033 2.857329e-02
#> 204 0.0158629290 -0.0189412224 1.702651e-02
#> 205 -0.0036010735 -0.0261576214 2.763588e-02
#> 206 -0.0212687130 -0.0394605273 7.407970e-02
#> 207 0.0105619971 -0.0226867080 2.168648e-02
#> 208 -0.0776674665 0.0507321487 7.253475e-02
#> 209 -0.0330271125 0.0320311931 1.082496e-02
#> 210 0.0072448367 -0.0225298740 2.727321e-03
#> 211 0.0024952402 -0.0270962764 2.750152e-02
#> 212 -0.0192850166 0.0283425246 8.471276e-03
#> 213 -0.0241399125 0.0221530443 9.253175e-03
#> 214 0.0016320746 -0.0158743625 -1.181062e-02
#> 215 0.0140249859 -0.0436593170 -2.151875e-02
#> 216 -0.0087475917 0.0282965084 6.519916e-03
#> 217 0.0406981440 -0.0232985124 -3.285404e-03
#> 218 0.0188001723 -0.0170423323 2.727106e-02
#> 219 -0.0220949939 -0.0575983999 -4.376584e-02
#> 220 0.0044258604 -0.0148088178 1.480410e-02
#> 221 -0.0166117087 0.0236672521 7.910138e-03
#> 222 -0.0223032796 -0.0364472324 9.439237e-03
#> 223 0.0926762964 -0.0369128518 -2.492383e-02
#> 224 -0.0641439711 0.0246405958 1.666007e-02
#> 225 0.0433683096 0.0094356190 1.811624e-02
#> 226 -0.0163049880 -0.0208684591 -1.240141e-02
#> 227 -0.0092500861 0.0171511025 6.199495e-03
#> 228 0.0095030791 -0.0237181596 2.452578e-03
#>
#> $influential_points
#> 3 6 18 33 37 38 71 85 89 129
#> 3 6 17 32 36 37 70 84 88 128
check_functional_form_coxph(model_cox)
#> [1] "Functional form check: Review plots of martingale residuals vs predictors for nonlinearity."
Conclusion
The modeldiag package provides a unified and extensible
framework for model diagnostics, combining statistical rigor with
practical usability.
By integrating multiple diagnostic tools into a consistent interface, it simplifies the process of validating model assumptions across diverse modeling frameworks.
References
Cook, R. D., & Weisberg, S. (1982). Residuals and Influence in Regression. Chapman & Hall.
Breusch, T. S., & Pagan, A. R. (1979). A Simple Test for Heteroscedasticity and Random Coefficient Variation. Econometrica.
Durbin, J., & Watson, G. S. (1950, 1951). Testing for Serial Correlation in Least Squares Regression. Biometrika.
Shapiro, S. S., & Wilk, M. B. (1965). An Analysis of Variance Test for Normality. Biometrika.
Hosmer, D. W., Lemeshow, S., & Sturdivant, R. X. (2013). Applied Logistic Regression. Wiley.
Cox, D. R. (1972). Regression Models and Life-Tables. JRSS.
Cameron, A. C., & Trivedi, P. K. (2013). Regression Analysis of Count Data. Cambridge University Press.