Skip to content

Latest commit

 

History

History
143 lines (102 loc) · 5.33 KB

UNMAINTAINED.md

File metadata and controls

143 lines (102 loc) · 5.33 KB
Raw

Unmaintained Functions

The functions in this section are undocumented. If you know what any of them mean and can help us to document, fix, and/or improve the code, please contact the maintainers.

stein1, stein2: Two steps of Stein's method

julia> stein1(x, 1)
41
julia> srand(1)         #set seed
julia> x2=rnorm(21);    #suppose additional 21 data points were collected.
julia> stein2(x, x2)
df:        19
estimate:  0.8441066102423266
confint:   [-3.65043, 5.33865]
statistic: 2.516970580783766
crit:      2.093024054408309
pval:      0.020975586092444765

stein1_tr(), stein2_tr()

Extension of Stein's method based on the trimmed mean.

julia> stein1_tr(x, 0.2)
89

julia> stein2_tr(x, x2)
Extension of the 2nd stage of Stein's method based on the trimmed mean

Statistic:            3.154993
Critical value:       2.200985

This function is able to handle multiple dependent groups. Suppose that the original dataset contained 4 dependent groups and the sample size is 5 (xold), and we collected more data (xnew).

julia> srand(2)
julia> xnew = rand(6, 4)
julia> xold = reshape(x, 5, 4)
julia> stein2_tr(xold, xnew)

Extension of the 2nd stage of Stein's method based on the trimmed mean

 Statistic             Group 1  Group 2  Statistic
                             1        2  -0.933245
                             1        3   0.291014
                             1        4  -0.949618
                             2        3   1.212577
                             2        4  -0.608510
                             3        4  -0.649426
 Critical value:       10.885867

akerd:

Compute adaptive kernel density estimate for univariate data (See Silverman, 1986)

 julia> akerd(x, title="Lognormal Distribution", xlab="x", ylab="Density")


 julia> srand(10)
 julia> x3=rnorm(100, 1, 2);
 julia> akerd(x3, title="Normal Distribution; mu=1, sd=2", xlab="x", ylab="Density", color="red", plottype="dash")

indirectTest:

This function is adapted from Andrew Hayes' SPSS macro, which evaluates indirect/mediation effects via percentile bootstrap and the Sobel Test.

 julia> srand(1)
 julia> m = randn(20);        #Mediator
 julia> srand(2)
 julia> y = randn(20) + 2.0;  #Outcome variable

 julia> indirectTest(y, x, m)   #5000 bootstrap samples by default
 TESTS OF INDIRECT EFFECT

 Sample size: 20
 Number of bootstrap samples: 5000

 DIRECT AND TOTAL EFFECTS
           Estimate  Std.Error     t value   Pr(>|t|)
 b(YX):    0.125248   0.087729    1.427664   0.170508
 b(MX):    0.082156   0.106198    0.773611   0.449202
 b(YM.X):  0.140675   0.089359    1.574264   0.133852
 b(YX.M): -0.187775   0.195111   -0.962402   0.349338

 INDIRECT EFFECT AND SIGNIFICANCE USING NORMAL DISTRIBUTION
           Estimate  Std.Error     z score      CI lo      CI hi  Pr(>|z|)
 Sobel:   -0.015427   0.019161   -0.805126  -0.052981   0.022128  0.420747

 BOOTSTRAP RESULTS OF INDIRECT EFFECT
           Estimate  Std.Error       CI lo      CI hi    P value
 Effect:  -0.048598   0.084280   -0.298647   0.019394   0.420800

if we add plotit=true, we get a kernel density plot of the effects derived from bootstrap samples:

t1way()

A heteroscedastic one-way ANOVA for trimmed means using a generalization of Welch's method. When tr=0, the function conducts a heteroscedastic 1-way ANOVA without trimming.

There are two ways to specify data for the function:

  • A two dimensional array where each column represents a group. Hence, a 10 X 3 array means that a one way ANOVA will be performed on 3 groups. This also means equal sample sizes amongst the groups.
  • A vector containing the outcome variable and another vector containing group information.

Two examples are shown below to demonstrate the two ways of specifying data:

#Data in two dimensional array form
#Prepare data
julia> srand(12)
julia> m2 = reshape(sort(randn(30)), 10, 3);

julia> t1way(m2)
Heteroscedastic one-way ANOVA for trimmed means
using a generalization of Welch's method.

Sample size:          10   10   10
Degrees of freedom:   2.00   8.25
Statistic:            20.955146
p value:              0.000583


#Data in vector form
julia> srand(12)
julia> m3 = sort(randn(30));
julia> group = rep(1:3, [8,12,10]);   #Unequal sample sizes: n1 = 8, n2 = 12, n3 = 10

julia> t1way(m3, group)
Heteroscedastic one-way ANOVA for trimmed means
using a generalization of Welch's method.

Sample size:          8   12   10
Degrees of freedom:   2.00   8.11
Statistic:            28.990510
p value:              0.000202

trimcibt

Compute a (1-α) confidence interval for the trimmed mean using a bootstrap percentile t method. The default amount of trimming is tr=.2. side=true, indicates the symmetric two-sided method. side=false yields an equal-tailed confidence interval. NOTE: p.value is reported when side=true only.

julia> trimcibt(x, nboot=5000)
Bootstrap .95 confidence interval for the trimmed mean
using a bootstrap percentile t method

 Estimate:             1.292180
 Statistic:            3.469611
 Confidence interval:  0.292162       2.292199
 p value:              0.022600