Run a Wald tests on discrete and continuous components hypothesis can be one of a character giving complete factors or terms to be dropped from the model, CoefficientHypothesis giving names of coefficients to be dropped, Hypothesis giving contrasts using the symbolically, or a contrast matrix, with one row for each coefficient in the full model, and one column for each contrast being tested.

waldTest(object, hypothesis)

Arguments

object

LMlike or subclass

hypothesis

the hypothesis to be tested. See details.

Value

array giving test statistics

See also

fit

lrTest

lht

Examples

#see ZlmFit-class for examples
example('ZlmFit-class')
#> 
#> ZlmFt-> data(vbetaFA)
#> 
#> ZlmFt-> zlmVbeta <- zlm(~ Stim.Condition+Population, subset(vbetaFA, ncells==1)[1:10,])
#> 
#> Done!
#> 
#> ZlmFt-> #Coefficients and standard errors
#> ZlmFt-> coef(zlmVbeta, 'D')
#>        (Intercept) Stim.ConditionUnstim PopulationCD154+VbetaUnresponsive
#> B3GAT1  -4.1795641           0.63282096                      -1.162182250
#> BAX     -0.9330077           0.02794714                      -0.162052054
#> BCL2    -3.9226304          -2.20112377                       1.332228054
#> CCL2    -3.8309742           0.54760417                       0.147212758
#> CCL3    -2.3287704          -1.94930881                      -0.567152079
#> CCL4    -2.9386008          -1.06755978                      -0.003368973
#> CCL5    -1.2350667           0.09455937                      -0.484094746
#> CCR2    -4.1050742           1.37877860                       1.504033462
#> CCR4    -0.1126440          -0.21758890                      -0.839917265
#> CCR5    -2.7417205          -1.20694083                       0.521925468
#>        PopulationCD154-VbetaResponsive PopulationCD154-VbetaUnresponsive
#> B3GAT1                     -1.14875333                       -0.16659777
#> BAX                         0.45518519                       -0.46291603
#> BCL2                       -1.29400053                       -0.39116499
#> CCL2                        0.84204812                        0.14680392
#> CCL3                       -0.14648827                       -0.60189062
#> CCL4                        0.02118041                       -1.25132594
#> CCL5                       -0.65755684                       -0.41313077
#> CCR2                        0.40289360                        0.39925195
#> CCR4                       -0.24604817                       -0.68742757
#> CCR5                       -0.16103855                        0.02099718
#>        PopulationVbetaResponsive PopulationVbetaUnresponsive
#> B3GAT1                -1.8211123                 -0.53512412
#> BAX                    0.5582425                  0.53846239
#> BCL2                   2.0919143                  1.91118512
#> CCL2                  -0.7797822                 -2.02874891
#> CCL3                  -0.7669146                 -2.46844725
#> CCL4                  -2.1491640                 -2.15309456
#> CCL5                  -0.8123545                 -0.94068157
#> CCR2                  -0.4731219                  0.18547502
#> CCR4                  -0.1364576                 -0.01272681
#> CCR5                  -0.5077805                 -0.12742084
#> 
#> ZlmFt-> coef(zlmVbeta, 'C')
#>        (Intercept) Stim.ConditionUnstim PopulationCD154+VbetaUnresponsive
#> B3GAT1    18.19441           -1.7969063                                NA
#> BAX       17.67008           -0.6534516                        -0.2356154
#> BCL2      18.73554            1.3286670                        -1.3753715
#> CCL2      23.94679           -7.3355989                        -3.6985974
#> CCL3      19.86182                   NA                         3.2750181
#> CCL4      19.54785                   NA                         1.2579223
#> CCL5      20.07363            0.4504418                        -0.2026483
#> CCR2      15.27429           -1.2269270                         4.1759840
#> CCR4      18.03446           -0.3702826                        -0.1011834
#> CCR5      16.28993            0.9461661                         1.1537964
#>        PopulationCD154-VbetaResponsive PopulationCD154-VbetaUnresponsive
#> B3GAT1                              NA                        -0.5500307
#> BAX                        -0.19649762                        -0.2783088
#> BCL2                                NA                        -3.1850947
#> CCL2                       -7.04188444                        -3.9220153
#> CCL3                       -0.04812137                        -0.6043503
#> CCL4                        2.77190815                        -2.5532715
#> CCL5                       -0.84757938                        -1.5303864
#> CCR2                        3.19304135                         4.0151403
#> CCR4                       -0.57583680                        -0.7602052
#> CCR5                       -0.51211945                        -0.6646556
#>        PopulationVbetaResponsive PopulationVbetaUnresponsive
#> B3GAT1                        NA                          NA
#> BAX                  -0.04213554                 -0.01140701
#> BCL2                 -1.58527659                 -2.32150932
#> CCL2                          NA                          NA
#> CCL3                  0.45944273                          NA
#> CCL4                          NA                          NA
#> CCL5                 -1.61445447                 -1.33608326
#> CCR2                  3.31403666                  2.07650762
#> CCR4                 -0.26166401                 -0.75331686
#> CCR5                 -1.26236131                 -1.52747203
#> 
#> ZlmFt-> se.coef(zlmVbeta, 'C')
#>         
#> X1       (Intercept) Stim.ConditionUnstim PopulationCD154+VbetaUnresponsive
#>   B3GAT1   1.1195139            1.9390550                                NA
#>   BAX      0.2289293            0.2625570                         0.4158706
#>   BCL2     1.1852624            1.2983899                         1.3686231
#>   CCL2     2.5224874            4.3690763                         4.3690763
#>   CCL3     1.4009323                   NA                         3.1325799
#>   CCL4     1.7441805                   NA                         3.2630629
#>   CCL5     0.4951370            1.0038683                         1.0106941
#>   CCR2     1.1047933            1.2757054                         1.2757054
#>   CCR4     0.2983985            0.4372988                         0.6361878
#>   CCR5     0.6656093            2.1048414                         0.9984140
#>         
#> X1       PopulationCD154-VbetaResponsive PopulationCD154-VbetaUnresponsive
#>   B3GAT1                              NA                         1.9390550
#>   BAX                          0.3643741                         0.3574157
#>   BCL2                                NA                         1.6762142
#>   CCL2                         3.5673358                         3.5673358
#>   CCL3                         2.6825812                         2.4264860
#>   CCL4                         3.2630629                         4.2723522
#>   CCL5                         1.0847908                         0.7768348
#>   CCR2                         1.5624136                         1.3530899
#>   CCR4                         0.5532457                         0.4774376
#>   CCR5                         1.2452410                         0.9413137
#>         
#> X1       PopulationVbetaResponsive PopulationVbetaUnresponsive
#>   B3GAT1                        NA                          NA
#>   BAX                    0.3211103                   0.3241627
#>   BCL2                   1.2670988                   1.2983899
#>   CCL2                          NA                          NA
#>   CCL3                   3.1325799                          NA
#>   CCL4                          NA                          NA
#>   CCL5                   1.0362222                   0.9807059
#>   CCR2                   1.8596442                   1.5624136
#>   CCR4                   0.4777267                   0.4725825
#>   CCR5                   1.6304032                   1.0869354
#> 
#> ZlmFt-> #Test for a Population effect by dropping the whole term (a 5 degree of freedom test)
#> ZlmFt-> lrTest(zlmVbeta, 'Population')
#> Refitting on reduced model...
#> 
#> Done!
#> , , metric = lambda
#> 
#>         test.type
#> primerid      cont      disc    hurdle
#>   B3GAT1  0.000000  3.293892  3.293892
#>   BAX     1.072472 10.728081 11.800553
#>   BCL2    5.443797 20.567934 26.011731
#>   CCL2    4.103765  4.775242  8.879007
#>   CCL3    1.523584  7.006491  8.530076
#>   CCL4    1.516648  8.444875  9.961523
#>   CCL5    5.572644  5.389674 10.962318
#>   CCR2   12.540757  4.640800 17.181557
#>   CCR4    4.607460  8.728194 13.335653
#>   CCR5    7.136405  1.526627  8.663031
#> 
#> , , metric = df
#> 
#>         test.type
#> primerid cont disc hurdle
#>   B3GAT1    0    5      5
#>   BAX       5    5     10
#>   BCL2      4    5      9
#>   CCL2      3    5      8
#>   CCL3      4    5      9
#>   CCL4      3    5      8
#>   CCL5      5    5     10
#>   CCR2      5    5     10
#>   CCR4      5    5     10
#>   CCR5      5    5     10
#> 
#> , , metric = Pr(>Chisq)
#> 
#>         test.type
#> primerid       cont         disc     hurdle
#>   B3GAT1 1.00000000 0.6547769674 0.65477697
#>   BAX    0.95651117 0.0570459966 0.29862654
#>   BCL2   0.24471407 0.0009773063 0.00203398
#>   CCL2   0.25047521 0.4439211826 0.35260548
#>   CCL3   0.82245576 0.2201579879 0.48173135
#>   CCL4   0.67843337 0.1333623010 0.26773693
#>   CCL5   0.35004597 0.3701952302 0.36046135
#>   CCR2   0.02808429 0.4612686366 0.07044188
#>   CCR4   0.46563569 0.1204092082 0.20550576
#>   CCR5   0.21069179 0.9099767975 0.56435354
#> 
#> attr(,"test")
#> [1] "Population"
#> 
#> ZlmFt-> #Test only if the VbetaResponsive cells differ from the baseline group
#> ZlmFt-> lrTest(zlmVbeta, CoefficientHypothesis('PopulationVbetaResponsive'))
#> Refitting on reduced model...
#> 
#> Done!
#> , , metric = lambda
#> 
#>         test.type
#> primerid       cont      disc     hurdle
#>   B3GAT1 0.00000000 2.2974635  2.2974635
#>   BAX    0.01776885 2.5081546  2.5259234
#>   BCL2   1.80508046 9.4881861 11.2932665
#>   CCL2   0.00000000 0.6678630  0.6678630
#>   CCL3   0.02425584 1.1530015  1.1772574
#>   CCL4   0.00000000 3.8914009  3.8914009
#>   CCL5   2.54893181 3.3702326  5.9191644
#>   CCR2   3.99053248 0.1406114  4.1311439
#>   CCR4   0.30752656 0.1884803  0.4960069
#>   CCR5   0.73461509 0.3702349  1.1048500
#> 
#> , , metric = df
#> 
#>         test.type
#> primerid cont disc hurdle
#>   B3GAT1    0    1      1
#>   BAX       1    1      2
#>   BCL2      1    1      2
#>   CCL2      0    1      1
#>   CCL3      1    1      2
#>   CCL4      0    1      1
#>   CCL5      1    1      2
#>   CCR2      1    1      2
#>   CCR4      1    1      2
#>   CCR5      1    1      2
#> 
#> , , metric = Pr(>Chisq)
#> 
#>         test.type
#> primerid      cont        disc      hurdle
#>   B3GAT1 1.0000000 0.129585466 0.129585466
#>   BAX    0.8939563 0.113258489 0.282815165
#>   BCL2   0.1790995 0.002067992 0.003529379
#>   CCL2   1.0000000 0.413797670 0.413797670
#>   CCL3   0.8762357 0.282921705 0.555087964
#>   CCL4   1.0000000 0.048533925 0.048533925
#>   CCL5   0.1103689 0.066384383 0.051840572
#>   CCR2   0.0457566 0.707673921 0.126745777
#>   CCR4   0.5792020 0.664184477 0.780357269
#>   CCR5   0.3913913 0.542876237 0.575552395
#> 
#> attr(,"test")
#> [1] "PopulationVbetaResponsive"
#> 
#> ZlmFt-> # Test if there is a difference between CD154+/Unresponsive and CD154-/Unresponsive.
#> ZlmFt-> # Note that because we parse the expression
#> ZlmFt-> # the columns must be enclosed in backquotes
#> ZlmFt-> # to protect the \quote{+} and \quote{-} characters.
#> ZlmFt-> lrTest(zlmVbeta, Hypothesis('`PopulationCD154+VbetaUnresponsive` -
#> ZlmFt-+         `PopulationCD154-VbetaUnresponsive`'))
#> Warning: Some levels contain symbols.  Be careful to escape these names with backticks ('`') when specifying contrasts.
#> Refitting on reduced model...
#> 
#> Done!
#> , , metric = lambda
#> 
#>         test.type
#> primerid        cont        disc     hurdle
#>   B3GAT1 0.000000000  0.19720610  0.1972061
#>   BAX    0.009603320  0.43127916  0.4408825
#>   BCL2   2.004979393  2.88482572  4.8898051
#>   CCL2   0.003581828 -0.10852740 -0.1049456
#>   CCL3   1.389919527 -0.59684167  0.7930779
#>   CCL4   0.695474388  1.22446841  1.9199428
#>   CCL5   1.643474587  0.01090422  1.6543788
#>   CCR2   0.037354159  1.44946742  1.4868216
#>   CCR4   0.977322744  0.13931993  1.1166427
#>   CCR5   3.776168456  0.50849269  4.2846611
#> 
#> , , metric = df
#> 
#>         test.type
#> primerid cont disc hurdle
#>   B3GAT1    0    1      1
#>   BAX       1    1      2
#>   BCL2      1    1      2
#>   CCL2      1    1      2
#>   CCL3      1    1      2
#>   CCL4      1    1      2
#>   CCL5      1    1      2
#>   CCR2      1    1      2
#>   CCR4      1    1      2
#>   CCR5      1    1      2
#> 
#> , , metric = Pr(>Chisq)
#> 
#>         test.type
#> primerid       cont       disc     hurdle
#>   B3GAT1 1.00000000 0.65698552 0.65698552
#>   BAX    0.92193505 0.51136195 0.80216477
#>   BCL2   0.15678342 0.08941768 0.08673459
#>   CCL2   0.95227640 1.00000000 1.00000000
#>   CCL3   0.23841869 1.00000000 0.67264409
#>   CCL4   0.40430856 0.26848550 0.38290384
#>   CCL5   0.19984941 0.91683346 0.43727657
#>   CCR2   0.84674577 0.22861343 0.47548935
#>   CCR4   0.32286067 0.70895803 0.57216874
#>   CCR5   0.05198758 0.47579209 0.11738096
#> 
#> attr(,"test")
#> [1] "Contrast Matrix"
#> 
#> ZlmFt-> waldTest(zlmVbeta, Hypothesis('`PopulationCD154+VbetaUnresponsive` -
#> ZlmFt-+         `PopulationCD154-VbetaUnresponsive`'))
#> Warning: Some levels contain symbols.  Be careful to escape these names with backticks ('`') when specifying contrasts.
#> , , metric = lambda
#> 
#>         test.type
#> primerid        cont         disc      hurdle
#>   B3GAT1          NA 2.632691e-01          NA
#>   BAX    0.009305455 4.373274e-01 0.446632837
#>   BCL2   1.748463371 2.500540e+00 4.249003565
#>   CCL2   0.002614910 1.215898e-07 0.002615031
#>   CCL3   1.278016527 1.692421e-03 1.279708948
#>   CCL4   0.636616606 1.271218e+00 1.907834528
#>   CCL5   1.553679693 1.810976e-02 1.571789452
#>   CCR2   0.025434721 1.431864e+00 1.457299039
#>   CCR4   0.955370495 1.297495e-01 1.085120034
#>   CCR5   3.317281808 5.264420e-01 3.843723848
#> 
#> , , metric = df
#> 
#>         test.type
#> primerid cont disc hurdle
#>   B3GAT1    1    1      2
#>   BAX       1    1      2
#>   BCL2      1    1      2
#>   CCL2      1    1      2
#>   CCL3      1    1      2
#>   CCL4      1    1      2
#>   CCL5      1    1      2
#>   CCR2      1    1      2
#>   CCR4      1    1      2
#>   CCR5      1    1      2
#> 
#> , , metric = Pr(>Chisq)
#> 
#>         test.type
#> primerid       cont      disc    hurdle
#>   B3GAT1         NA 0.6078831        NA
#>   BAX    0.92315144 0.5084152 0.7998617
#>   BCL2   0.18607002 0.1138073 0.1194925
#>   CCL2   0.95921700 0.9997218 0.9986933
#>   CCL3   0.25826815 0.9671850 0.5273692
#>   CCL4   0.42493864 0.2595383 0.3852290
#>   CCL5   0.21259304 0.8929499 0.4557118
#>   CCR2   0.87328861 0.2314604 0.4825602
#>   CCR4   0.32835604 0.7186919 0.5812583
#>   CCR5   0.06855509 0.4681066 0.1463342
#>