tests/testthat/test_6_randomforest.R
In andykrause/hpiR: House Price Indexes
#*****************************************************************************************
#
# Unit tests for hpiR package - Random Forest Method
#
#*****************************************************************************************
library(hpiR)
library(testthat)
## Load Data
data(ex_sales)
hed_df <- hedCreateTrans(trans_df = ex_sales,
prop_id='pinx',
trans_id='sale_id',
price='sale_price',
date='sale_date',
periodicity='monthly')
context('hpiModel.heddata(): before hedModel()')
test_that('hpi Model with Hed works', {
# Dep/Ind variety
expect_is(rf_model <- hpiModel(model_type= 'rf',
hpi_df = hed_df,
estimator = 'pdp',
dep_var = 'price',
ind_var = c('tot_sf', 'beds', 'baths'),
log_dep = TRUE,
ntrees= 10,
sim_count = 10),
'hpimodel')
# Full formula
expect_is(rf_model <- hpiModel(model_type = 'rf',
hpi_df = hed_df,
estimator = 'pdp',
mod_spec = as.formula(paste0('price ~ baths + tot_sf')),
log_dep = TRUE,
ntrees= 10,
sim_count = 10),
'hpimodel')
})
test_that('"log_dep" works both ways',{
expect_true(hpiModel(model_type = 'rf',
hpi_df = hed_df,
estimator = 'pdp',
dep_var = 'price',
ind_var = c('tot_sf', 'beds', 'baths'),
log_dep = FALSE,
ntrees = 10,
sim_count = 10)$model_obj$predictions[1] > 100)
expect_true(hpiModel(model_type = 'rf',
hpi_df = hed_df,
estimator = 'pdp',
dep_var = 'price',
ind_var = c('tot_sf', 'beds', 'baths'),
log_dep = TRUE,
ntrees = 10,
sim_count = 10)$model_obj$predictions[1] < 100)
})
test_that('Check for zero or negative prices works',{
hed_dfx <- hed_df
hed_dfx$price[1] <- 0
# 0 in prices with Log Dep
expect_error(rf_model <- hpiModel(model_type = 'rf',
hpi_df = hed_dfx,
estimator = 'pdp',
dep_var = 'price',
ind_var = c('tot_sf', 'beds', 'baths'),
log_dep = TRUE))
# 0 in prices with no Log Dep (Works)
expect_is(rf_model <- hpiModel(model_type = 'rf',
hpi_df = hed_dfx,
estimator = 'pdp',
dep_var = 'price',
ind_var = c('tot_sf', 'beds', 'baths'),
log_dep = FALSE,
ntrees = 10,
sim_count = 10),
'hpimodel')
## NA
hed_dfx$price[1] <- NA_integer_
# NA in prices with Log Dep
expect_error(rf_model <- hpiModel(model_type = 'rf',
hpi_df = hed_dfx,
estimator = 'pdp',
dep_var = 'price',
ind_var = c('tot_sf', 'beds', 'baths'),
log_dep = TRUE))
## INF
hed_dfx$price[1] <- Inf
# Inf in prices with Log Dep
expect_error(rf_model <- hpiModel(model_type = 'rf',
hpi_df = hed_dfx,
estimator = 'pdp',
dep_var = 'price',
ind_var = c('tot_sf', 'beds', 'baths'),
log_dep = TRUE))
})
### hedModel() ---------------------------------------------------------------------------
context('rfModel()')
test_that('Check for errors with bad arguments',{
# Return warning if wrong rf_df
expect_error(rf_model <- rfModel(rf_df = ex_sales,
estimator = structure('pdp', class='pdp'),
rf_spec = as.formula(paste0('log(price) ~ ',
'as.factor(baths) + tot_sf'))))
# Bad spec
expect_error(rf_model <- rfModel(rf_df = hed_df,
rf_spec = as.formula(paste0('log(x) ~ ',
'as.factor(baths) + tot_sf')),
estimator=structure('pdp', class='pdp')))
# Bad estimator class
expect_error(rf_model <- hedModel(rf_df = hed_df,
rf_spec = as.formula(paste0('log(price) ~ ',
'baths + tot_sf')),
estimator = structure('fobust', class='fobust')))
})
test_that('Performance with sparse data',{
## Moderate Sparseness
# Create a sparse data set
hed_df200 <- hed_df[1:200, ]
# Works
expect_is(rf_model <- rfModel(rf_df = hed_df200,
estimator = structure('pdp', class='pdp'),
rf_spec = as.formula(paste0('log(price) ~ ',
'baths + tot_sf'))),
'rfmodel')
## Check severe sparseness
# Create data set
hed_df20 <- hed_df[1:20, ]
# Works
expect_is(rf_model <- rfModel(rf_df = hed_df20,
estimator = structure('pdp', class='pdp'),
rf_spec = as.formula(paste0('log(price) ~ ',
'baths + tot_sf'))),
'rfmodel')
})
### hpiModel.rf after hedModel --------------------------------------------------------
context('hpiModel.rf()')
test_that('hpiModel.rf works in both trim_model cases', {
expect_is(rf_model <- hpiModel(model_type = 'rf',
hpi_df = hed_df,
estimator = 'pdp',
log_dep = TRUE,
dep_var = 'price',
ind_var = c('tot_sf', 'beds', 'baths'),
trim_model=TRUE,
ntrees = 10,
sim_count = 10), 'hpimodel')
expect_is(rf_model$model_obj$forest, 'NULL')
})
test_that('hpiModel.heddata outputs are correct', {
# Run a model of each estimator type
rf_model <- hpiModel(model_type = 'rf',
hpi_df = hed_df,
estimator = 'pdp',
dep_var = 'price',
ind_var = c('tot_sf', 'beds', 'baths'),
log_dep = TRUE,
trim_model = TRUE,
ntrees = 10,
sim_count = 10)
# Estimatohed
expect_is(rf_model$estimator, 'pdp')
# Coefficients
expect_is(rf_model$coefficients, 'data.frame')
expect_true(nrow(rf_model$coefficients) == 84)
# Modelobj
expect_is(rf_model$model_obj, 'rfmodel')
# Model spec
expect_true(is.null(rf_model$model_spec))
# base price
expect_true(round(rf_model$base_price, 0) == 618792)
# Periods
expect_is(rf_model$periods, 'data.frame')
expect_true(nrow(rf_model$periods) == 84)
# Approach
expect_true(rf_model$approach == 'rf')
})
### modelToIndex() (HED) --------------------------------------------------------------------
context('modelToIndex(): hed')
hed_model <- hpiModel(model_type = 'hed',
hpi_df = hed_df,
estimator = 'base',
log_dep = TRUE,
trim_model=TRUE,
dep_var = 'price',
ind_var = c('tot_sf', 'beds', 'baths'))
test_that('modelToIndex works', {
expect_is(modelToIndex(hed_model), 'hpiindex')
})
test_that('modelToIndex works with other estimators and options', {
# Robust, LogDep=T, TrimModel=T
expect_is(modelToIndex(hpiModel(model_type = 'rf',
hpi_df = hed_df,
estimator = 'pdp',
log_dep = TRUE,
trim_model = TRUE,
ntrees = 10,
sim_count = 10,
dep_var = 'price',
ind_var = c('tot_sf', 'beds', 'baths'))),
'hpiindex')
})
### smoothIndex() -------------------------------------------------------------
context('smoothIndex()')
model_pdp <- hpiModel(model_type = 'rf',
hpi_df = hed_df,
estimator = 'pdp',
log_dep = TRUE,
trim_model=TRUE,
sim_count = 10,
ntrees = 10,
dep_var = 'price',
ind_var = c('tot_sf', 'beds', 'baths'))
index_pdp <- modelToIndex(model_obj = model_pdp)
test_that('smoothing Function works with a variety of inputs',{
# HPI Index object
expect_is(index_smooth <- smoothIndex(index_obj = index_pdp,
order = 4),
'indexsmooth')
})
### hedIndex() wrapper ---------------------------------------------------------------
context('rfindex() wrapper')
test_that('Function works with proper inputs',{
# Full case
full_1 <- rfIndex(trans_df = ex_sales,
date = 'sale_date',
price = 'sale_price',
trans_id = 'sale_id',
prop_id = 'pinx',
estimator = 'pdp',
periodicity = 'monthly',
dep_var = 'price',
ind_var = c('tot_sf', 'beds', 'baths'),
sim_count = 10,
ntrees = 10)
expect_is(full_1, 'hpi')
expect_true(full_1$model$estimator == 'pdp')
# Giving an 'rs_df' object
full_2 <- rfIndex(trans_df = hed_df,
estimator = 'pdp',
log_dep = FALSE,
rf_spec = as.formula(price ~ baths + beds),
sim_count = 10,
ntrees = 10)
expect_is(full_2, 'hpi')
expect_true(full_2$model$estimator == 'pdp')
# Giving an 'rs_df' object
full_3 <- rfIndex(trans_df = hed_df,
estimator = 'pdp',
log_dep = FALSE,
rf_spec = as.formula(price ~ baths + beds),
sim_count = 10,
ntrees = 10,
smooth = TRUE,
smooth_order = 5)
expect_is(full_3, 'hpi')
expect_true(full_3$model$estimator == 'pdp')
})
test_that('Additional arguments in hedIndex() work',{
## HED Create arguments
# Min Date Model with Clip
addarg_index <- rfIndex(trans_df = ex_sales,
date='sale_date',
price = 'sale_price',
trans_id = 'sale_id',
prop_id = 'pinx',
estimator = 'pdp',
dep_var = 'price',
ind_var = c('tot_sf', 'beds', 'baths'),
min_date = as.Date('2011-01-01'),
max_date = as.Date('2015-12-31'),
periodicity = 'annual',
adj_type = 'clip',
sim_per = 0.01,
ntrees = 17)
expect_is(addarg_index, 'hpi')
expect_true(addarg_index$index$name[1] == '2011')
})
test_that("Bad arguments generate Errors: Full Case",{
# Bad Date
expect_error(rfIndex(trans_df = ex_sales,
date = 'sale_price',
price = 'sale_price',
trans_id = 'sale_id',
prop_id = 'pinx',
estimator = 'pdp',
log_dep = TRUE,
dep_var = 'price',
ind_var = c('tot_sf', 'beds', 'baths'),
periodicity = 'monthly'))
expect_error(rfIndex(trans_df = ex_sales,
date = 'sale_date',
trans_id = 'sale_id',
prop_id = 'pinx',
estimator = 'pdp',
log_dep = TRUE,
dep_var = 'price',
ind_var = c('tot_sf', 'beds', 'baths'),
periodicity = 'monthly'))
expect_error(rfIndex(trans_df = sales_df,
price = 'xx',
trans_id = 'sale_id',
prop_id = 'pinx',
estimator = 'pdp',
log_dep = TRUE,
dep_var = 'price',
ind_var = c('tot_sf', 'beds', 'baths')))
expect_error(rfIndex(trans_df = sales_df,
price = 'sale_price',
prop_id = 'pinx',
estimator = 'pdp',
log_dep = TRUE,
dep_var = 'price',
ind_var = c('tot_sf', 'beds', 'baths')))
expect_error(rfIndex(trans_df = sales_df,
price = 'sale+price',
trans_id = 'sale_id',
estimator = 'pdp',
log_dep = TRUE,
dep_var = 'price',
ind_var = c('tot_sf', 'beds', 'baths')))
expect_error(rfIndex(trans_df = ex_sales,
date = 'sale_date',
price = 'sale_price',
trans_id = 'sale_id',
prop_id = 'pinx',
estimator = 'pdp',
log_dep = TRUE,
periodicity = 'monthly'))
})
test_that("Smoothing in_place for 'hpi' object works",{
# Full case
full_1 <- rfIndex(trans_df = ex_sales,
date = 'sale_date',
price = 'sale_price',
trans_id = 'sale_id',
prop_id = 'pinx',
estimator = 'pdp',
periodicity = 'monthly',
dep_var = 'price',
ind_var = c('tot_sf', 'beds', 'baths'),
smooth = TRUE,
sim_ids = 1:10,
ntrees = 16)
# In wrapper smoothing worked
expect_is(full_1$index$smooth, 'indexsmooth')
# Full HPI Object
expect_is(index_smooth <- smoothIndex(index_obj = full_1,
order = 6),
'indexsmooth')
# Add it to the Full HPI Object (to the hpiindex object) with new name
expect_is(full_1s <- smoothIndex(index = full_1,
order = 3,
in_place = TRUE),
'hpi')
expect_is(full_1s$index$smooth, 'ts')
expect_is(full_1s$index$smooth, 'indexsmooth')
})
#*****************************************************************************************
#*****************************************************************************************
andykrause/hpiR documentation built on Feb. 2, 2024, 8:13 p.m.
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#*****************************************************************************************
#
# Unit tests for hpiR package - Random Forest Method
#
#*****************************************************************************************
library(hpiR)
library(testthat)
## Load Data
data(ex_sales)
hed_df <- hedCreateTrans(trans_df = ex_sales,
prop_id='pinx',
trans_id='sale_id',
price='sale_price',
date='sale_date',
periodicity='monthly')
context('hpiModel.heddata(): before hedModel()')
test_that('hpi Model with Hed works', {
# Dep/Ind variety
expect_is(rf_model <- hpiModel(model_type= 'rf',
hpi_df = hed_df,
estimator = 'pdp',
dep_var = 'price',
ind_var = c('tot_sf', 'beds', 'baths'),
log_dep = TRUE,
ntrees= 10,
sim_count = 10),
'hpimodel')
# Full formula
expect_is(rf_model <- hpiModel(model_type = 'rf',
hpi_df = hed_df,
estimator = 'pdp',
mod_spec = as.formula(paste0('price ~ baths + tot_sf')),
log_dep = TRUE,
ntrees= 10,
sim_count = 10),
'hpimodel')
})
test_that('"log_dep" works both ways',{
expect_true(hpiModel(model_type = 'rf',
hpi_df = hed_df,
estimator = 'pdp',
dep_var = 'price',
ind_var = c('tot_sf', 'beds', 'baths'),
log_dep = FALSE,
ntrees = 10,
sim_count = 10)$model_obj$predictions[1] > 100)
expect_true(hpiModel(model_type = 'rf',
hpi_df = hed_df,
estimator = 'pdp',
dep_var = 'price',
ind_var = c('tot_sf', 'beds', 'baths'),
log_dep = TRUE,
ntrees = 10,
sim_count = 10)$model_obj$predictions[1] < 100)
})
test_that('Check for zero or negative prices works',{
hed_dfx <- hed_df
hed_dfx$price[1] <- 0
# 0 in prices with Log Dep
expect_error(rf_model <- hpiModel(model_type = 'rf',
hpi_df = hed_dfx,
estimator = 'pdp',
dep_var = 'price',
ind_var = c('tot_sf', 'beds', 'baths'),
log_dep = TRUE))
# 0 in prices with no Log Dep (Works)
expect_is(rf_model <- hpiModel(model_type = 'rf',
hpi_df = hed_dfx,
estimator = 'pdp',
dep_var = 'price',
ind_var = c('tot_sf', 'beds', 'baths'),
log_dep = FALSE,
ntrees = 10,
sim_count = 10),
'hpimodel')
## NA
hed_dfx$price[1] <- NA_integer_
# NA in prices with Log Dep
expect_error(rf_model <- hpiModel(model_type = 'rf',
hpi_df = hed_dfx,
estimator = 'pdp',
dep_var = 'price',
ind_var = c('tot_sf', 'beds', 'baths'),
log_dep = TRUE))
## INF
hed_dfx$price[1] <- Inf
# Inf in prices with Log Dep
expect_error(rf_model <- hpiModel(model_type = 'rf',
hpi_df = hed_dfx,
estimator = 'pdp',
dep_var = 'price',
ind_var = c('tot_sf', 'beds', 'baths'),
log_dep = TRUE))
})
### hedModel() ---------------------------------------------------------------------------
context('rfModel()')
test_that('Check for errors with bad arguments',{
# Return warning if wrong rf_df
expect_error(rf_model <- rfModel(rf_df = ex_sales,
estimator = structure('pdp', class='pdp'),
rf_spec = as.formula(paste0('log(price) ~ ',
'as.factor(baths) + tot_sf'))))
# Bad spec
expect_error(rf_model <- rfModel(rf_df = hed_df,
rf_spec = as.formula(paste0('log(x) ~ ',
'as.factor(baths) + tot_sf')),
estimator=structure('pdp', class='pdp')))
# Bad estimator class
expect_error(rf_model <- hedModel(rf_df = hed_df,
rf_spec = as.formula(paste0('log(price) ~ ',
'baths + tot_sf')),
estimator = structure('fobust', class='fobust')))
})
test_that('Performance with sparse data',{
## Moderate Sparseness
# Create a sparse data set
hed_df200 <- hed_df[1:200, ]
# Works
expect_is(rf_model <- rfModel(rf_df = hed_df200,
estimator = structure('pdp', class='pdp'),
rf_spec = as.formula(paste0('log(price) ~ ',
'baths + tot_sf'))),
'rfmodel')
## Check severe sparseness
# Create data set
hed_df20 <- hed_df[1:20, ]
# Works
expect_is(rf_model <- rfModel(rf_df = hed_df20,
estimator = structure('pdp', class='pdp'),
rf_spec = as.formula(paste0('log(price) ~ ',
'baths + tot_sf'))),
'rfmodel')
})
### hpiModel.rf after hedModel --------------------------------------------------------
context('hpiModel.rf()')
test_that('hpiModel.rf works in both trim_model cases', {
expect_is(rf_model <- hpiModel(model_type = 'rf',
hpi_df = hed_df,
estimator = 'pdp',
log_dep = TRUE,
dep_var = 'price',
ind_var = c('tot_sf', 'beds', 'baths'),
trim_model=TRUE,
ntrees = 10,
sim_count = 10), 'hpimodel')
expect_is(rf_model$model_obj$forest, 'NULL')
})
test_that('hpiModel.heddata outputs are correct', {
# Run a model of each estimator type
rf_model <- hpiModel(model_type = 'rf',
hpi_df = hed_df,
estimator = 'pdp',
dep_var = 'price',
ind_var = c('tot_sf', 'beds', 'baths'),
log_dep = TRUE,
trim_model = TRUE,
ntrees = 10,
sim_count = 10)
# Estimatohed
expect_is(rf_model$estimator, 'pdp')
# Coefficients
expect_is(rf_model$coefficients, 'data.frame')
expect_true(nrow(rf_model$coefficients) == 84)
# Modelobj
expect_is(rf_model$model_obj, 'rfmodel')
# Model spec
expect_true(is.null(rf_model$model_spec))
# base price
expect_true(round(rf_model$base_price, 0) == 618792)
# Periods
expect_is(rf_model$periods, 'data.frame')
expect_true(nrow(rf_model$periods) == 84)
# Approach
expect_true(rf_model$approach == 'rf')
})
### modelToIndex() (HED) --------------------------------------------------------------------
context('modelToIndex(): hed')
hed_model <- hpiModel(model_type = 'hed',
hpi_df = hed_df,
estimator = 'base',
log_dep = TRUE,
trim_model=TRUE,
dep_var = 'price',
ind_var = c('tot_sf', 'beds', 'baths'))
test_that('modelToIndex works', {
expect_is(modelToIndex(hed_model), 'hpiindex')
})
test_that('modelToIndex works with other estimators and options', {
# Robust, LogDep=T, TrimModel=T
expect_is(modelToIndex(hpiModel(model_type = 'rf',
hpi_df = hed_df,
estimator = 'pdp',
log_dep = TRUE,
trim_model = TRUE,
ntrees = 10,
sim_count = 10,
dep_var = 'price',
ind_var = c('tot_sf', 'beds', 'baths'))),
'hpiindex')
})
### smoothIndex() -------------------------------------------------------------
context('smoothIndex()')
model_pdp <- hpiModel(model_type = 'rf',
hpi_df = hed_df,
estimator = 'pdp',
log_dep = TRUE,
trim_model=TRUE,
sim_count = 10,
ntrees = 10,
dep_var = 'price',
ind_var = c('tot_sf', 'beds', 'baths'))
index_pdp <- modelToIndex(model_obj = model_pdp)
test_that('smoothing Function works with a variety of inputs',{
# HPI Index object
expect_is(index_smooth <- smoothIndex(index_obj = index_pdp,
order = 4),
'indexsmooth')
})
### hedIndex() wrapper ---------------------------------------------------------------
context('rfindex() wrapper')
test_that('Function works with proper inputs',{
# Full case
full_1 <- rfIndex(trans_df = ex_sales,
date = 'sale_date',
price = 'sale_price',
trans_id = 'sale_id',
prop_id = 'pinx',
estimator = 'pdp',
periodicity = 'monthly',
dep_var = 'price',
ind_var = c('tot_sf', 'beds', 'baths'),
sim_count = 10,
ntrees = 10)
expect_is(full_1, 'hpi')
expect_true(full_1$model$estimator == 'pdp')
# Giving an 'rs_df' object
full_2 <- rfIndex(trans_df = hed_df,
estimator = 'pdp',
log_dep = FALSE,
rf_spec = as.formula(price ~ baths + beds),
sim_count = 10,
ntrees = 10)
expect_is(full_2, 'hpi')
expect_true(full_2$model$estimator == 'pdp')
# Giving an 'rs_df' object
full_3 <- rfIndex(trans_df = hed_df,
estimator = 'pdp',
log_dep = FALSE,
rf_spec = as.formula(price ~ baths + beds),
sim_count = 10,
ntrees = 10,
smooth = TRUE,
smooth_order = 5)
expect_is(full_3, 'hpi')
expect_true(full_3$model$estimator == 'pdp')
})
test_that('Additional arguments in hedIndex() work',{
## HED Create arguments
# Min Date Model with Clip
addarg_index <- rfIndex(trans_df = ex_sales,
date='sale_date',
price = 'sale_price',
trans_id = 'sale_id',
prop_id = 'pinx',
estimator = 'pdp',
dep_var = 'price',
ind_var = c('tot_sf', 'beds', 'baths'),
min_date = as.Date('2011-01-01'),
max_date = as.Date('2015-12-31'),
periodicity = 'annual',
adj_type = 'clip',
sim_per = 0.01,
ntrees = 17)
expect_is(addarg_index, 'hpi')
expect_true(addarg_index$index$name[1] == '2011')
})
test_that("Bad arguments generate Errors: Full Case",{
# Bad Date
expect_error(rfIndex(trans_df = ex_sales,
date = 'sale_price',
price = 'sale_price',
trans_id = 'sale_id',
prop_id = 'pinx',
estimator = 'pdp',
log_dep = TRUE,
dep_var = 'price',
ind_var = c('tot_sf', 'beds', 'baths'),
periodicity = 'monthly'))
expect_error(rfIndex(trans_df = ex_sales,
date = 'sale_date',
trans_id = 'sale_id',
prop_id = 'pinx',
estimator = 'pdp',
log_dep = TRUE,
dep_var = 'price',
ind_var = c('tot_sf', 'beds', 'baths'),
periodicity = 'monthly'))
expect_error(rfIndex(trans_df = sales_df,
price = 'xx',
trans_id = 'sale_id',
prop_id = 'pinx',
estimator = 'pdp',
log_dep = TRUE,
dep_var = 'price',
ind_var = c('tot_sf', 'beds', 'baths')))
expect_error(rfIndex(trans_df = sales_df,
price = 'sale_price',
prop_id = 'pinx',
estimator = 'pdp',
log_dep = TRUE,
dep_var = 'price',
ind_var = c('tot_sf', 'beds', 'baths')))
expect_error(rfIndex(trans_df = sales_df,
price = 'sale+price',
trans_id = 'sale_id',
estimator = 'pdp',
log_dep = TRUE,
dep_var = 'price',
ind_var = c('tot_sf', 'beds', 'baths')))
expect_error(rfIndex(trans_df = ex_sales,
date = 'sale_date',
price = 'sale_price',
trans_id = 'sale_id',
prop_id = 'pinx',
estimator = 'pdp',
log_dep = TRUE,
periodicity = 'monthly'))
})
test_that("Smoothing in_place for 'hpi' object works",{
# Full case
full_1 <- rfIndex(trans_df = ex_sales,
date = 'sale_date',
price = 'sale_price',
trans_id = 'sale_id',
prop_id = 'pinx',
estimator = 'pdp',
periodicity = 'monthly',
dep_var = 'price',
ind_var = c('tot_sf', 'beds', 'baths'),
smooth = TRUE,
sim_ids = 1:10,
ntrees = 16)
# In wrapper smoothing worked
expect_is(full_1$index$smooth, 'indexsmooth')
# Full HPI Object
expect_is(index_smooth <- smoothIndex(index_obj = full_1,
order = 6),
'indexsmooth')
# Add it to the Full HPI Object (to the hpiindex object) with new name
expect_is(full_1s <- smoothIndex(index = full_1,
order = 3,
in_place = TRUE),
'hpi')
expect_is(full_1s$index$smooth, 'ts')
expect_is(full_1s$index$smooth, 'indexsmooth')
})
#*****************************************************************************************
#*****************************************************************************************
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