Description Usage Arguments Details Value Author(s) References See Also Examples
conTestScore
tests linear equality and/or
inequality restricted hypotheses for (robust) linear models by scoretests. It can be
used directly and is called by the conTest
function if test = "score"
.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17  ## S3 method for class 'conLM'
conTestScore(object, type = "A", neq.alt = 0,
boot = "no", R = 9999, p.distr = rnorm,
parallel = "no", ncpus = 1L, cl = NULL, seed = 1234,
verbose = FALSE, control = NULL, ...)
## S3 method for class 'conRLM'
conTestScore(object, type = "A", neq.alt = 0,
boot = "no", R = 9999, p.distr = rnorm,
parallel = "no", ncpus = 1L, cl = NULL, seed = 1234,
verbose = FALSE, control = NULL, ...)
## S3 method for class 'conGLM'
conTestScore(object, type = "A", neq.alt = 0,
boot = "no", R = 9999, p.distr = rnorm,
parallel = "no", ncpus = 1L, cl = NULL, seed = 1234,
verbose = FALSE, control = NULL, ...)

object 
an object of class 
type 
hypothesis test type "A", "B", "C", "global", or "summary" (default). See details for more information. 
neq.alt 
integer: number of equality constraints that are maintained under the alternative hypothesis (for hypothesis test type "B"), see example 3. 
boot 
the nulldistribution of these teststatistics
(except under type "C", see details) takes the form of a mixture of
Fdistributions. The tail probabilities can be computed directly
via bootstrapping; if 
R 
integer; number of bootstrap draws for 
p.distr 
random generation distribution for the parametric bootstrap. For
all available distributions see 
parallel 
the type of parallel operation to be used (if any). If missing, the default is set "no". 
ncpus 
integer: number of processes to be used in parallel operation: typically one would chose this to the number of available CPUs. 
cl 
an optional parallel or snow cluster for use if parallel = "snow". If not supplied, a cluster on the local machine is created for the duration of the conTest call. 
seed 
seed value. The default value is set to 1234. 
verbose 
logical; if TRUE, information is shown at each bootstrap draw. 
control 
a list of control arguments:

... 
additional arguments to be passed to the p.distr function. 
The following hypothesis tests are available:
Type A: Test H0: all constraints with equalities ("=") active against HA: at least one inequality restriction (">") strictly true.
Type B: Test H0: all constraints with inequalities (">") (including some equalities ("=")) active against HA: at least one restriction false (some equality constraints may be maintained).
Type C: Test H0: at least one restriction false ("<") against HA: all constraints strikty true (">"). This test is based on the intersectionunion principle (Silvapulle and Sen, 2005, chp 5.3). Note that, this test only makes sense in case of no equality constraints.
Type global: equal to Type A but H0 contains additional equality constraints. This test is analogue to the global Ftest in lm, where all coefficients but the intercept equal 0.
The nulldistribution of hypothesis test Type C is based on a tdistribution (onesided). Its power can be poor in case of many inequalty constraints. Its main role is to prevent wrong conclusions from significant results from hypothesis test Type A.
The exact finite sample distributions of the nonrobust F,
score and LRtest statistics based on restricted OLS estimates
and normally distributed errors, are a mixture of Fdistributions
under the null hypothesis (Wolak, 1987). In agreement with
Silvapulle (1992), we found that the results based on these
mixtures of Fdistributions approximate the tail probabilities of
the robust tests better than their asymptotic distributions.
Therefore, all pvalues for hypothesis test Type "A"
,
"B"
and "global"
are computed based on mixtures of
Fdistributions.
An object of class conTest, for which a print is available. More specifically, it is a list with the following items:
CON 
a list with useful information about the constraints. 
Amat 
constraints matrix. 
bvec 
vector of righthand side elements. 
meq 
number of equality constraints. 
meq.alt 
same as input neq.alt. 
iact 
number of active constraints. 
type 
same as input. 
test 
same as input. 
Ts 
teststatistic value. 
df.residual 
the residual degrees of freedom. 
pvalue 
tail probability for 
b.eqrestr 
equality restricted regression coefficients.
Only available for 
b.unrestr 
unrestricted regression coefficients. 
b.restr 
restricted regression coefficients. 
b.restr.alt 
restricted regression coefficients under HA
if some equality constraints are maintained. Only available for

Sigma 
variancecovariance matrix of unrestricted model. 
R2.org 
unrestricted Rsquared, not available for objects of class 
R2.reduced 
restricted Rsquared, not available for objects of class 
boot 
same as input. 
model.org 
original model. 
Leonard Vanbrabant and Yves Rosseel
Silvapulle, M. and Silvapulle, P. (1995). A score test against onesided alternatives. American statistical association, 90, 342–349.
Silvapulle, M. (1996) Robust bounded influence tests against onesided hypotheses in general parametric models. Statistics & probability letters, 31, 45–50.
Silvapulle, M.J. and Sen, P.K. (2005). Constrained Statistical Inference. Wiley, New York
quadprog,
conTest
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129  ## example 1:
# the data consist of ages (in months) at which an
# infant starts to walk alone.
# prepare data
DATA1 < subset(ZelazoKolb1972, Group != "Control")
# fit unrestricted linear model
fit1.lm < lm(Age ~ 1 + Group, data = DATA1)
# the variable names can be used to impose constraints on
# the corresponding regression parameters.
coef(fit1.lm)
# constraint syntax: assuming that the walking
# exercises would not have a negative effect of increasing the
# mean age at which a child starts to walk.
myConstraints1 < ' GroupActive < GroupPassive;
GroupPassive < GroupNo '
conTest(fit1.lm, myConstraints1, test = "score")
# another way is to first fit the restricted model
fit.restr1 < restriktor(fit1.lm, constraints = myConstraints1)
conTest(fit.restr1, test = "score")
## Not run:
# Or in matrix notation.
Amat1 < rbind(c(1, 0, 1),
c( 0, 1, 1))
myRhs1 < rep(0L, nrow(Amat1))
myNeq1 < 0
conTest(fit1.lm, constraints = Amat1, test = "score",
rhs = myRhs1, neq = myNeq1)
## End(Not run)
#########################
## Artificial examples ##
#########################
# generate data
n < 10
means < c(1,2,1,3)
nm < length(means)
group < as.factor(rep(1:nm, each = n))
y < rnorm(n * nm, rep(means, each = n))
DATA2 < data.frame(y, group)
# fit unrestricted linear model
fit2.lm < lm(y ~ 1 + group, data = DATA2)
coef(fit2.lm)
## example 2: increasing means
myConstraints2 < ' group1 < group2
group2 < group3
group3 < group4 '
# compute Ftest for hypothesis test Type A and compute the tail
# probability based on the parametric bootstrap. We only generate 9
# bootstrap samples in this example; in practice you may wish to
# use a much higher number.
conTest(fit2.lm, constraints = myConstraints2, type = "A", test = "score",
boot = "parametric", R = 9)
# or fit restricted linear model
fit2.con < restriktor(fit2.lm, constraints = myConstraints2)
conTest(fit2.con, test = "score")
## Not run:
# increasing means in matrix notation.
Amat2 < rbind(c(1, 1, 0, 0),
c( 0,1, 1, 0),
c( 0, 0,1, 1))
myRhs2 < rep(0L, nrow(Amat2))
myNeq2 < 0
conTest(fit2.con, constraints = Amat2, rhs = myRhs2, neq = myNeq2,
type = "A", test = "score", boot = "parametric", R = 9)
## End(Not run)
## example 3:
# combination of equality and inequality constraints.
myConstraints3 < ' group1 == group2
group3 < group4 '
conTest(fit2.lm, constraints = myConstraints3, type = "B", test = "score", neq.alt = 1)
# fit resticted model and compute modelbased bootstrapped
# standard errors. We only generate 9 bootstrap samples in this
# example; in practice you may wish to use a much higher number.
# Note that, a warning message may be thrown because the number of
# bootstrap samples is too low.
fit3.con < restriktor(fit2.lm, constraints = myConstraints3,
se = "boot.model.based", B = 9)
conTest(fit3.con, type = "B", test = "score", neq.alt = 1)
## example 4:
# restriktor can also be used to define effects using the := operator
# and impose constraints on them. For example, is the
# average effect (AVE) larger than zero?
# generate data
n < 30
b0 < 10; b1 = 0.5; b2 = 1; b3 = 1.5
X < c(rep(c(0), n/2), rep(c(1), n/2))
set.seed(90)
Z < rnorm(n, 16, 5)
y < b0 + b1*X + b2*Z + b3*X*Z + rnorm(n, 0, sd = 10)
DATA3 = data.frame(cbind(y, X, Z))
# fit linear model with interaction
fit4.lm < lm(y ~ X*Z, data = DATA3)
# constraint syntax
myConstraints4 < ' AVE := X + 16.86137*X.Z;
AVE > 0 '
conTest(fit4.lm, constraints = myConstraints4, test = "score")
# or
fit4.con < restriktor(fit4.lm, constraints = ' AVE := X + 16.86137*X.Z;
AVE > 0 ')
conTest(fit4.con, test = "score")

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