Results - KS Test


Spatial Covariance Structure

Linear Mixed Model

Theoretical Residuals

Kolmogorov-Smirnov Test
Linear Mixed Model. Distribution of theoretical p-values under the correct (A) and mis-specified (B-D) models evaluated under the Kolmogorov-Smirnov Test for each method when true parameters are known. Mis-specification are, from left to right: Missing Random Effect (B), Normal data fit to Gamma (C), Mis-specified Random Effect (D).

Linear Mixed Model. Distribution of theoretical p-values under the correct (A) and mis-specified (B-D) models evaluated under the Kolmogorov-Smirnov Test for each method when true parameters are known. Mis-specification are, from left to right: Missing Random Effect (B), Normal data fit to Gamma (C), Mis-specified Random Effect (D).

Anderson-Darling Test
Linear Mixed Model. Distribution of theoretical p-values under the correct (A) and mis-specified (B-D) models evaluated under the Anderson-Darling Test for each method when true parameters are known. Mis-specification are, from left to right: Missing Random Effect (B), Normal data fit to Lognormal (C), Mis-specified Random Effect (D).

Linear Mixed Model. Distribution of theoretical p-values under the correct (A) and mis-specified (B-D) models evaluated under the Anderson-Darling Test for each method when true parameters are known. Mis-specification are, from left to right: Missing Random Effect (B), Normal data fit to Lognormal (C), Mis-specified Random Effect (D).

Spatial Autocorrelation Test
Linear Mixed Model. Distribution of theoretical p-values under the correct (A) and mis-specified (B-D) models evaluated under the Moran's I Spatial Correlation Test for each method when true parameters are known. Mis-specification are, from left to right: Missing Random Effect (B), Normal data fit to Lognormal (C), Mis-specified Random Effect (D).

Linear Mixed Model. Distribution of theoretical p-values under the correct (A) and mis-specified (B-D) models evaluated under the Moran’s I Spatial Correlation Test for each method when true parameters are known. Mis-specification are, from left to right: Missing Random Effect (B), Normal data fit to Lognormal (C), Mis-specified Random Effect (D).


Estimated Residuals

Kolmogorov-Smirnov
Linear Mixed Model. Distribution of estimated p-values under the correct (A) and mis-specified (B-D) models evaluated under the Kolmogorov-Smirnov Test for each method when parameters are estimated. Mis-specification are, from left to right: Missing Random Effect (B), Normal data fit to Lognormal (C), Mis-specified Random Effect (D).

Linear Mixed Model. Distribution of estimated p-values under the correct (A) and mis-specified (B-D) models evaluated under the Kolmogorov-Smirnov Test for each method when parameters are estimated. Mis-specification are, from left to right: Missing Random Effect (B), Normal data fit to Lognormal (C), Mis-specified Random Effect (D).

Lilliefors
Linear Mixed Model. Distribution of estimated p-values under the correct (A) and mis-specified (B-D) models evaluated under the Lilliefors Test for each method when parameters are estimated. Mis-specification are, from left to right: Missing Random Effect (B), Normal data fit to Lognormal (C), Mis-specified Random Effect (D).

Linear Mixed Model. Distribution of estimated p-values under the correct (A) and mis-specified (B-D) models evaluated under the Lilliefors Test for each method when parameters are estimated. Mis-specification are, from left to right: Missing Random Effect (B), Normal data fit to Lognormal (C), Mis-specified Random Effect (D).


Anderson-Darling Test
Linear Mixed Model. Distribution of estimated p-values under the correct (A) and mis-specified (B-D) models evaluated under the Anderson-Darling Test for each method when parameters are estimated. Mis-specification are, from left to right: Missing Random Effect (B), Normal data fit to Lognormal (C),Mis-specified Random Effect (D).

Linear Mixed Model. Distribution of estimated p-values under the correct (A) and mis-specified (B-D) models evaluated under the Anderson-Darling Test for each method when parameters are estimated. Mis-specification are, from left to right: Missing Random Effect (B), Normal data fit to Lognormal (C),Mis-specified Random Effect (D).

Spatial Autocorrelation Test
Linear Mixed Model. Distribution of estimated p-values under the correct (A) and mis-specified (B-D) models evaluated under the Moran's I spatial autocorrelation test for each method when parameters are estimated. Mis-specification are, from left to right: Missing Random Effect (B), Normal data fit to Lognormal (C), Mis-specified Random Effect (D).

Linear Mixed Model. Distribution of estimated p-values under the correct (A) and mis-specified (B-D) models evaluated under the Moran’s I spatial autocorrelation test for each method when parameters are estimated. Mis-specification are, from left to right: Missing Random Effect (B), Normal data fit to Lognormal (C), Mis-specified Random Effect (D).


Generalized Linear Mixed Model

Theoretical Residuals

Kolmogorov-Smirnov Test
Generalized Linear Mixed Model. Distribution of theoretical p-values under the correct (A) and mis-specified (B-D) models evaluated under the Kolmogorov-Smirnov Test for each method when true parameters are known. Mis-specification are, from left to right: Missing Random Effect (B), Gamma data fit to Lognormal (C), Mis-specified Random Effect (D).

Generalized Linear Mixed Model. Distribution of theoretical p-values under the correct (A) and mis-specified (B-D) models evaluated under the Kolmogorov-Smirnov Test for each method when true parameters are known. Mis-specification are, from left to right: Missing Random Effect (B), Gamma data fit to Lognormal (C), Mis-specified Random Effect (D).

Anderson-Darling Test
Generalized Linear Mixed Model. Distribution of theoretical p-values under the correct (A) and mis-specified (B-D) models evaluated under the Anderson-Darling Test for each method when true parameters are known. Mis-specification are, from left to right: Missing Random Effect (B), Gamma data fit to Lognormal (C), Mis-specified Random Effect (D).

Generalized Linear Mixed Model. Distribution of theoretical p-values under the correct (A) and mis-specified (B-D) models evaluated under the Anderson-Darling Test for each method when true parameters are known. Mis-specification are, from left to right: Missing Random Effect (B), Gamma data fit to Lognormal (C), Mis-specified Random Effect (D).

Spatial Autocorrelation Test
Generalized Linear Mixed Model. Distribution of theoretical p-values under the correct (A) and mis-specified (B-D) models evaluated under the Moran's I Spatial Correlation Test for each method when true parameters are known. Mis-specification are, from left to right: Missing Random Effect (B), Gamma data fit to Lognormal (C), Mis-specified Random Effect (D).

Generalized Linear Mixed Model. Distribution of theoretical p-values under the correct (A) and mis-specified (B-D) models evaluated under the Moran’s I Spatial Correlation Test for each method when true parameters are known. Mis-specification are, from left to right: Missing Random Effect (B), Gamma data fit to Lognormal (C), Mis-specified Random Effect (D).


Estimated Residuals

Kolmogorov-Smirnov
Generalized Linear Mixed Model. Distribution of estimated p-values under the correct (A) and mis-specified (B-D) models evaluated under the Kolmogorov-Smirnov Test for each method when parameters are estimated. Mis-specification are, from left to right: Missing Random Effect (B), Gamma data fit to Lognormal (C), Mis-specified Random Effect (D).

Generalized Linear Mixed Model. Distribution of estimated p-values under the correct (A) and mis-specified (B-D) models evaluated under the Kolmogorov-Smirnov Test for each method when parameters are estimated. Mis-specification are, from left to right: Missing Random Effect (B), Gamma data fit to Lognormal (C), Mis-specified Random Effect (D).

Lilliefors
Generalized Linear Mixed Model. Distribution of estimated p-values under the correct (A) and mis-specified (B-D) models evaluated under the Lilliefors Test for each method when parameters are estimated. Mis-specification are, from left to right: Missing Random Effect (B), Gamma data fit to Lognormal (C), Mis-specified Random Effect (D).

Generalized Linear Mixed Model. Distribution of estimated p-values under the correct (A) and mis-specified (B-D) models evaluated under the Lilliefors Test for each method when parameters are estimated. Mis-specification are, from left to right: Missing Random Effect (B), Gamma data fit to Lognormal (C), Mis-specified Random Effect (D).


Anderson-Darling Test
Generalized Linear Mixed Model. Distribution of estimated p-values under the correct (A) and mis-specified (B-D) models evaluated under the Anderson-Darling Test for each method when parameters are estimated. Mis-specification are, from left to right: Missing Random Effect (B), Gamma data fit to Lognormal (C), Mis-specified Random Effect (D).

Generalized Linear Mixed Model. Distribution of estimated p-values under the correct (A) and mis-specified (B-D) models evaluated under the Anderson-Darling Test for each method when parameters are estimated. Mis-specification are, from left to right: Missing Random Effect (B), Gamma data fit to Lognormal (C), Mis-specified Random Effect (D).

Spatial Autocorrelation Test
Generalized Linear Mixed Model. Distribution of estimated p-values under the correct (A) and mis-specified (B-D) models evaluated under the Moran's I spatial autocorrelation test for each method when parameters are estimated. Mis-specification are, from left to right: Missing Random Effect (B), Gamma data fit to Lognormal (C), Mis-specified Random Effect (D).

Generalized Linear Mixed Model. Distribution of estimated p-values under the correct (A) and mis-specified (B-D) models evaluated under the Moran’s I spatial autocorrelation test for each method when parameters are estimated. Mis-specification are, from left to right: Missing Random Effect (B), Gamma data fit to Lognormal (C), Mis-specified Random Effect (D).