Test of functional form assumption using B-splines

Estimate hypothesis test of lower- and higher-order non-linear relationships against an assumed target relationship.

NKnotsTest(
  form,
  var,
  data,
  targetdf = 1,
  degree = 3,
  min.knots = 1,
  max.knots = 10,
  adjust = "none"
)

Arguments

form	A formula detailing the model for which smoothing is to be evaluated.
var	A character string identifying the variable for which smoothing is to be evaluated.
data	Data frame providing values of all variables in `form`.
targetdf	The assumed degrees of freedom against which the tests will be conducted.
degree	Degree of polynomial in B-spline basis functions.
min.knots	Minimum number of internal B-spline knots to be evaluated.
max.knots	Maximum number of internal B-spline knots to be evaluated.
adjust	Method by which p-values will be adjusted (see `p.adjust`)

Value

A matrix with the following columns:

F statistics of test of candidate models against target model

DF1

Numerator DF from F-test

DF2

Denominator DF from F-test

p(F)

p-value from the F-test

Clarke

Test statistic from the Clarke test

Pr(Better)

The Clarke statistic divided by the number of observations

p(Clarke)

p-value from the Clarke test. (T) means that the significant p-value is in favor of the Target model and (C) means the significant p-value is in favor of the candidate (alternative) model.

Delta_AIC

AIC(candidate model) - AIC(target model)

Delta_AICc

AICc(candidate model) - AICc(target model)

Delta_BIC

BIC(candidate model) - BIC(target model)

Examples


data(Prestige, package="carData")
NKnotsTest(prestige ~ education + type, var="income", data=na.omit(Prestige), targetdf=3)
#>                F      DF1 DF2 p(F)  Clarke Pr(Better) p(Clarke) Delta_AIC
#> DF=3 vs. DF=1  6.962* 2   91  0.002 47     0.480      0.762     9.953    
#> DF=3 vs. DF=2  5.211* 1   91  0.025 44     0.449      0.363     3.457    
#>    Target                                                                
#> DF=3 vs. DF=4  1.140  1   90  0.289 66*    0.673      0.001 (T) 0.767    
#> DF=3 vs. DF=5  0.735  2   89  0.483 72*    0.735      0.000 (T) 2.396    
#> DF=3 vs. DF=6  0.540  3   88  0.656 77*    0.786      0.000 (T) 4.211    
#> DF=3 vs. DF=7  0.378  4   87  0.824 81*    0.827      0.000 (T) 6.313    
#> DF=3 vs. DF=8  0.463  5   86  0.803 80*    0.816      0.000 (T) 7.399    
#> DF=3 vs. DF=9  0.356  6   85  0.905 81*    0.827      0.000 (T) 9.570    
#> DF=3 vs. DF=10 0.631  7   84  0.729 82*    0.837      0.000 (T) 8.981    
#> DF=3 vs. DF=11 0.483  8   83  0.865 82*    0.837      0.000 (T) 11.538   
#> DF=3 vs. DF=12 0.557  9   82  0.828 83*    0.847      0.000 (T) 12.185   
#> DF=3 vs. DF=13 0.524  10  81  0.869 85*    0.867      0.000 (T) 13.859   
#>                Delta_AICc Delta_BIC
#> DF=3 vs. DF=1  9.258      4.783    
#> DF=3 vs. DF=2  3.083      0.872    
#>    Target                          
#> DF=3 vs. DF=4  1.194      3.352    
#> DF=3 vs. DF=5  3.306      7.565    
#> DF=3 vs. DF=6  5.663      11.966   
#> DF=3 vs. DF=7  8.365      16.653   
#> DF=3 vs. DF=8  10.115     20.324   
#> DF=3 vs. DF=9  13.012     25.080   
#> DF=3 vs. DF=10 13.217     27.076   
#> DF=3 vs. DF=11 16.636     32.218   
#> DF=3 vs. DF=12 18.217     35.450   
#> DF=3 vs. DF=13 20.899     39.709

Test of functional form assumption using B-splines

Arguments

Value

Examples

Contents

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