Lack-of-fit test for models fitted to data with replicates

Source: R/loftest.R

This is a generic function with a method currently only defined for mkinfit objects. It fits an anova model to the data contained in the object and compares the likelihoods using the likelihood ratio test lrtest.default from the lmtest package.

loftest(object, ...)

# S3 method for mkinfit
loftest(object, ...)

Arguments

object

A model object with a defined loftest method
...

Not used

Details

The anova model is interpreted as the simplest form of an mkinfit model, assuming only a constant variance about the means, but not enforcing any structure of the means, so we have one model parameter for every mean of replicate samples.

See also

lrtest

Examples

# \dontrun{
test_data <- subset(synthetic_data_for_UBA_2014[[12]]$data, name == "parent")
sfo_fit <- mkinfit("SFO", test_data, quiet = TRUE)
plot_res(sfo_fit) # We see a clear pattern in the residuals

loftest(sfo_fit)  # We have a clear lack of fit

#> Likelihood ratio test
#> 
#> Model 1: ANOVA with error model const
#> Model 2: SFO with error model const
#>   #Df  LogLik Df  Chisq Pr(>Chisq)    
#> 1  10 -40.710                         
#> 2   3 -63.954 -7 46.487  7.027e-08 ***
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#
# We try a different model (the one that was used to generate the data)
dfop_fit <- mkinfit("DFOP", test_data, quiet = TRUE)
plot_res(dfop_fit) # We don't see systematic deviations, but heteroscedastic residuals

# therefore we should consider adapting the error model, although we have
loftest(dfop_fit) # no lack of fit

#> Likelihood ratio test
#> 
#> Model 1: ANOVA with error model const
#> Model 2: DFOP with error model const
#>   #Df  LogLik Df Chisq Pr(>Chisq)
#> 1  10 -40.710                    
#> 2   5 -42.453 -5 3.485     0.6257
#
# This is the anova model used internally for the comparison
test_data_anova <- test_data
test_data_anova$time <- as.factor(test_data_anova$time)
anova_fit <- lm(value ~ time, data = test_data_anova)
summary(anova_fit)

#> 
#> Call:
#> lm(formula = value ~ time, data = test_data_anova)
#> 
#> Residuals:
#>     Min      1Q  Median      3Q     Max 
#> -6.1000 -0.5625  0.0000  0.5625  6.1000 
#> 
#> Coefficients:
#>             Estimate Std. Error t value Pr(>|t|)    
#> (Intercept)  103.150      2.323  44.409 7.44e-12 ***
#> time1        -19.950      3.285  -6.073 0.000185 ***
#> time3        -50.800      3.285 -15.465 8.65e-08 ***
#> time7        -68.500      3.285 -20.854 6.28e-09 ***
#> time14       -79.750      3.285 -24.278 1.63e-09 ***
#> time28       -86.000      3.285 -26.181 8.35e-10 ***
#> time60       -94.900      3.285 -28.891 3.48e-10 ***
#> time90       -98.500      3.285 -29.986 2.49e-10 ***
#> time120     -100.450      3.285 -30.580 2.09e-10 ***
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#> 
#> Residual standard error: 3.285 on 9 degrees of freedom
#> Multiple R-squared:  0.9953,	Adjusted R-squared:  0.9912 
#> F-statistic: 240.5 on 8 and 9 DF,  p-value: 1.417e-09
#> 
logLik(anova_fit) # We get the same likelihood and degrees of freedom

#> 'log Lik.' -40.71015 (df=10)
#
test_data_2 <- synthetic_data_for_UBA_2014[[12]]$data
m_synth_SFO_lin <- mkinmod(parent = list(type = "SFO", to = "M1"),
  M1 = list(type = "SFO", to = "M2"),
  M2 = list(type = "SFO"), use_of_ff = "max")

#> Temporary DLL for differentials generated and loaded
sfo_lin_fit <- mkinfit(m_synth_SFO_lin, test_data_2, quiet = TRUE)
plot_res(sfo_lin_fit) # not a good model, we try parallel formation

loftest(sfo_lin_fit)

#> Likelihood ratio test
#> 
#> Model 1: ANOVA with error model const
#> Model 2: m_synth_SFO_lin with error model const and fixed parameter(s) M1_0, M2_0
#>   #Df   LogLik  Df  Chisq Pr(>Chisq)    
#> 1  28  -93.606                          
#> 2   7 -171.927 -21 156.64  < 2.2e-16 ***
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#
m_synth_SFO_par <- mkinmod(parent = list(type = "SFO", to = c("M1", "M2")),
  M1 = list(type = "SFO"),
  M2 = list(type = "SFO"), use_of_ff = "max")

#> Temporary DLL for differentials generated and loaded
sfo_par_fit <- mkinfit(m_synth_SFO_par, test_data_2, quiet = TRUE)
plot_res(sfo_par_fit) # much better for metabolites

loftest(sfo_par_fit)

#> Likelihood ratio test
#> 
#> Model 1: ANOVA with error model const
#> Model 2: m_synth_SFO_par with error model const and fixed parameter(s) M1_0, M2_0
#>   #Df   LogLik  Df  Chisq Pr(>Chisq)    
#> 1  28  -93.606                          
#> 2   7 -156.331 -21 125.45  < 2.2e-16 ***
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#
m_synth_DFOP_par <- mkinmod(parent = list(type = "DFOP", to = c("M1", "M2")),
  M1 = list(type = "SFO"),
  M2 = list(type = "SFO"), use_of_ff = "max")

#> Temporary DLL for differentials generated and loaded
dfop_par_fit <- mkinfit(m_synth_DFOP_par, test_data_2, quiet = TRUE)
plot_res(dfop_par_fit) # No visual lack of fit

loftest(dfop_par_fit)  # no lack of fit found by the test

#> Likelihood ratio test
#> 
#> Model 1: ANOVA with error model const
#> Model 2: m_synth_DFOP_par with error model const and fixed parameter(s) M1_0, M2_0
#>   #Df   LogLik  Df  Chisq Pr(>Chisq)
#> 1  28  -93.606                      
#> 2   9 -102.763 -19 18.313     0.5016
#
# The anova model used for comparison in the case of transformation products
test_data_anova_2 <- dfop_par_fit$data
test_data_anova_2$variable <- as.factor(test_data_anova_2$variable)
test_data_anova_2$time <- as.factor(test_data_anova_2$time)
anova_fit_2 <- lm(observed ~ time:variable - 1, data = test_data_anova_2)
summary(anova_fit_2)

#> 
#> Call:
#> lm(formula = observed ~ time:variable - 1, data = test_data_anova_2)
#> 
#> Residuals:
#>     Min      1Q  Median      3Q     Max 
#> -6.1000 -0.5875  0.0000  0.5875  6.1000 
#> 
#> Coefficients: (2 not defined because of singularities)
#>                        Estimate Std. Error t value Pr(>|t|)    
#> time0:variableparent    103.150      1.573  65.562  < 2e-16 ***
#> time1:variableparent     83.200      1.573  52.882  < 2e-16 ***
#> time3:variableparent     52.350      1.573  33.274  < 2e-16 ***
#> time7:variableparent     34.650      1.573  22.024  < 2e-16 ***
#> time14:variableparent    23.400      1.573  14.873 6.35e-14 ***
#> time28:variableparent    17.150      1.573  10.901 5.47e-11 ***
#> time60:variableparent     8.250      1.573   5.244 1.99e-05 ***
#> time90:variableparent     4.650      1.573   2.956 0.006717 ** 
#> time120:variableparent    2.700      1.573   1.716 0.098507 .  
#> time0:variableM1             NA         NA      NA       NA    
#> time1:variableM1         11.850      1.573   7.532 6.93e-08 ***
#> time3:variableM1         22.700      1.573  14.428 1.26e-13 ***
#> time7:variableM1         33.050      1.573  21.007  < 2e-16 ***
#> time14:variableM1        31.250      1.573  19.863  < 2e-16 ***
#> time28:variableM1        18.900      1.573  12.013 7.02e-12 ***
#> time60:variableM1         7.550      1.573   4.799 6.28e-05 ***
#> time90:variableM1         3.850      1.573   2.447 0.021772 *  
#> time120:variableM1        2.050      1.573   1.303 0.204454    
#> time0:variableM2             NA         NA      NA       NA    
#> time1:variableM2          6.700      1.573   4.259 0.000254 ***
#> time3:variableM2         16.750      1.573  10.646 8.93e-11 ***
#> time7:variableM2         25.800      1.573  16.399 6.89e-15 ***
#> time14:variableM2        28.600      1.573  18.178 6.35e-16 ***
#> time28:variableM2        25.400      1.573  16.144 9.85e-15 ***
#> time60:variableM2        21.600      1.573  13.729 3.81e-13 ***
#> time90:variableM2        17.800      1.573  11.314 2.51e-11 ***
#> time120:variableM2       14.100      1.573   8.962 2.79e-09 ***
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#> 
#> Residual standard error: 2.225 on 25 degrees of freedom
#> Multiple R-squared:  0.9979,	Adjusted R-squared:  0.9957 
#> F-statistic: 469.2 on 25 and 25 DF,  p-value: < 2.2e-16
#> 
# }