Please don’t mind this post. I use this to try out various highlighting styles for my code and formats.
\begin{algorithm} \caption{Quicksort} \begin{algorithmic} \PROCEDURE{Quicksort}{$A, p, r$} \IF{$p < r$} \STATE $q = $ \CALL{Partition}{$A, p, r$} \STATE \CALL{Quicksort}{$A, p, q - 1$} \STATE \CALL{Quicksort}{$A, q + 1, r$} \ENDIF \ENDPROCEDURE \PROCEDURE{Partition}{$A, p, r$} \STATE $x = A[r]$ \STATE $i = p - 1$ \FOR{$j = p$ \TO $r - 1$} \IF{$A[j] < x$} \STATE $i = i + 1$ \STATE exchange $A[i]$ with $A[j]$ \ENDIF \STATE exchange $A[i]$ with $A[r]$ \ENDFOR \ENDPROCEDURE \end{algorithmic} \end{algorithm}
\[Y^{\operatorname{Post}} = \beta_{0} + \beta_{1}^{\operatorname{Group}} + \beta_{2}^{\operatorname{Base}} + \beta_{3}^{\operatorname{Age}} + \beta_{4}^{\operatorname{Z}} + \beta_{5}^{\operatorname{R1}} + \beta_{6}^{\operatorname{R2}} + \epsilon\]
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Stan
data {
int<lower=0> J; // number of schools
real y[J]; // estimated treatment effects
real<lower=0> sigma[J]; // standard error of effect estimates
}
parameters {
real mu; // population treatment effect
real<lower=0> tau; // standard deviation in treatment effects
vector[J] eta; // unscaled deviation from mu by school
}
transformed parameters {
vector[J] theta = mu + tau * eta; // school treatment effects
}
model {
target += normal_lpdf(eta | 0, 1); // prior log-density
target += normal_lpdf(y | theta, sigma); // log-likelihood
}
df1 <- read.csv("/Users/zad/Dropbox/LessLikely/ts.csv")
df1$y <- ts(df1$Sales)
df1$ds <- as.Date(df1$Time.Increment)
splits <- initial_time_split(df1, prop = 0.5)
train <- training(splits)
test <- testing(splits)
interactive <- TRUE
# Forecasting with auto.arima
library("forecast")
md <- auto.arima(train$y)
fc <- forecast(md, h = 12)
model_fit_arima_no_boost <- arima_reg() %>%
set_engine(engine = "auto_arima") %>%
fit(y ~ ds, data = training(splits))
# Model 2: arima_boost ----
model_fit_arima_boosted <- arima_boost(
min_n = 2,
learn_rate = 0.015
) %>%
set_engine(engine = "auto_arima_xgboost") %>%
fit(y ~ ds + as.numeric(ds) + factor(month(ds, label = TRUE),
ordered = F
),
data = training(splits)
)
# Model 3: ets ----
model_fit_ets <- exp_smoothing() %>%
set_engine(engine = "ets") %>%
fit(y ~ ds, data = training(splits))
model_fit_lm <- linear_reg() %>%
set_engine("lm") %>%
fit(y ~ as.numeric(ds) + factor(month(ds, label = TRUE),
ordered = FALSE
),
data = training(splits)
)
# Model 4: prophet ----
model_fit_prophet <- prophet_reg() %>%
set_engine(engine = "prophet") %>%
fit(y ~ ds, data = training(splits))
#> Error in sampler$call_sampler(c(args, dotlist)): c++ exception (unknown reason)
# Model 6: earth ----
model_spec_mars <- mars(mode = "regression") %>%
set_engine("earth")
recipe_spec <- recipe(y ~ ds, data = training(splits)) %>%
step_date(ds, features = "month", ordinal = FALSE) %>%
step_mutate(date_num = as.numeric(ds)) %>%
step_normalize(date_num) %>%
step_rm(ds)
wflw_fit_mars <- workflow() %>%
add_recipe(recipe_spec) %>%
add_model(model_spec_mars) %>%
fit(training(splits))
models_tbl <- modeltime_table(
model_fit_arima_no_boost,
model_fit_arima_boosted,
model_fit_ets,
model_fit_prophet,
model_fit_lm,
wflw_fit_mars
)
#> Error in eval(expr, envir, enclos): object 'model_fit_prophet' not found
calibration_tbl <- models_tbl %>%
modeltime_calibrate(new_data = testing(splits))
#> Error in eval(expr, envir, enclos): object 'models_tbl' not found
calibration_tbl %>%
modeltime_forecast(
new_data = testing(splits),
actual_data = df1
) %>%
plot_modeltime_forecast(
.legend_max_width = 25, # For mobile screens
.interactive = interactive
)
#> Error in eval(expr, envir, enclos): object 'calibration_tbl' not found
calibration_tbl %>%
modeltime_accuracy() %>%
table_modeltime_accuracy(
.interactive = FALSE
)
#> Error in eval(expr, envir, enclos): object 'calibration_tbl' not found
refit_tbl <- calibration_tbl %>%
modeltime_refit(data = df1)
#> Error in eval(expr, envir, enclos): object 'calibration_tbl' not found
refit_tbl %>%
modeltime_forecast(h = "4 years", actual_data = df1) %>%
plot_modeltime_forecast(
.legend_max_width = 10, # For mobile screens
.interactive = TRUE
)
#> Error in eval(expr, envir, enclos): object 'refit_tbl' not found
plot(greybox::forecast(smooth::adam(df1$y, h = 12, holdout = TRUE)))
plot(greybox::forecast(smooth::es(df1$y, h = 12, holdout = TRUE,
silent = FALSE)))
#> Forming the pool of models based on... ANN , AAN , Estimation progress: 100 %... Done!
s1 <- bayesforecast::stan_naive(ts = df1$y, chains = 4, iter = 4000,
cores = 8)
plot(s1) + theme_bw()
check_residuals(s1) + theme_light()
#> NULL
autoplot(object = forecast(s1, h = 12, biasadj = TRUE, PI = TRUE),
include = 100) + theme_bw()
autoplot(object = forecast(s1, h = 52, biasadj = TRUE, PI = TRUE),
include = 100) + theme_bw()
ztable(summary(s1))
mean | se | 5% | 95% | ess | Rhat | |
---|---|---|---|---|---|---|
mu0 | -0.03 | 0.03 | -4.74 | 4.83 | 7372 | 1 |
sigma0 | 4653.33 | 7.44 | 3708.33 | 5859.98 | 8197 | 1 |
loglik | -200.58 | 0.01 | -202.81 | -199.71 | 7858 | 1 |
(meanf(df1$y))
#> Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
#> 22 19920 10522 29317 5129 34711
#> 23 19920 10522 29317 5129 34711
#> 24 19920 10522 29317 5129 34711
#> 25 19920 10522 29317 5129 34711
#> 26 19920 10522 29317 5129 34711
#> 27 19920 10522 29317 5129 34711
#> 28 19920 10522 29317 5129 34711
#> 29 19920 10522 29317 5129 34711
#> 30 19920 10522 29317 5129 34711
#> 31 19920 10522 29317 5129 34711
(forecast(s1, h = 12))
#> Point Forecast Lo 0.8 Hi 0.8 Lo 0.9 Hi 0.9
#> 22 20125 14287 25777 12749 27859
#> 23 19835 13738 25666 12344 27816
#> 24 19843 14036 25487 12545 27291
#> 25 20184 14274 26250 12347 27730
#> 26 20172 14303 26204 12326 28149
#> 27 20072 14204 26124 12339 27832
#> 28 19833 13799 25685 12255 27674
#> 29 19750 13908 25689 12208 27450
#> 30 20011 14221 25871 12116 27355
#> 31 20211 14312 26164 12607 27934
#> 32 19819 13700 25833 11533 27400
#> 33 19777 14244 25598 11596 26884
autoplot(object = forecast(s1, h = 6, biasadj = TRUE, PI = TRUE),
include = 100) + theme_bw()
df <- as.data.frame(df1)
m <- prophet(df1, growth = "linear", yearly.seasonality = "auto")
#> Error in sampler$call_sampler(c(args, dotlist)): c++ exception (unknown reason)
future <- make_future_dataframe(m, periods = 60, freq = "months",
include_history = TRUE)
#> Error in eval(expr, envir, enclos): object 'm' not found
forecast <- predict(m, future)
#> Error in eval(expr, envir, enclos): object 'm' not found
plot(m, forecast) + theme_bw()
#> Error in h(simpleError(msg, call)): error in evaluating the argument 'x' in selecting a method for function 'plot': object 'm' not found
plot(greybox::forecast(smooth::auto.adam(df1$y, h = 12, holdout = TRUE,
ic = "AICc", regressors = "select")))
adamAutoARIMAAir <- auto.adam(df1$y, h = 50)
plot(greybox::forecast(adam(df1$y, main = "Parametric prediction interval",
h = 5, sim = 1000, lev = 0.99, interval = "prediction")))
plot(greybox::forecast(auto.adam(df1$y, h = 5, interval = "complete",
nsim = 100, main = "Complete prediction interval")))
plot(greybox::forecast(adam(df1$y, c("CCN", "ANN", "AAN", "AAdN"),
h = 10, holdout = TRUE, ic = "AICc")))
plot(greybox::forecast(adam(df1$y, model = "NNN", lags = 7, orders = c(0,
1, 1), constant = TRUE, h = 5, interval = "complete", nsim = 100)))
plot(greybox::forecast((adam(df1$y, model = "NNN", lags = c(24,
24 * 7, 24 * 365), orders = list(ar = c(3, 2, 2, 2), i = c(2,
1, 1, 1), ma = c(3, 2, 2, 2), select = TRUE), initial = "backcasting"))))
adamARIMA
#> Error in eval(expr, envir, enclos): object 'adamARIMA' not found
# Apply models
adamPoolBJ <- vector("list", 3)
adamPoolBJ[[1]] <- adam(df1$y, "ZZN", h = 10, holdout = TRUE,
ic = "BICc")
adamPoolBJ[[2]] <- adam(df1$y, "NNN", orders = list(ar = 3, i = 2,
ma = 3, select = TRUE), h = 10, holdout = TRUE, ic = "BICc")
adamPoolBJ[[3]] <- adam(df1$y, "MMN", h = 10, holdout = TRUE,
ic = "BICc", regressors = "select")
# Extract BICc values
adamsICs <- sapply(adamPoolBJ, BICc)
# Calculate weights
adamsICWeights <- adamsICs - min(adamsICs)
adamsICWeights[] <- exp(-0.5 * adamsICWeights)/sum(exp(-0.5 *
adamsICWeights))
names(adamsICWeights) <- c("ETS", "ARIMA", "ETSX")
round(adamsICWeights, 3)
#> ETS ARIMA ETSX
#> 0.087 0.913 0.000
adamPoolBJForecasts <- vector("list", 3)
# Produce forecasts from the three models
for (i in 1:3) {
adamPoolBJForecasts[[i]] <- forecast(adamPoolBJ[[i]], h = 10,
interval = "pred")
}
# Produce combined conditional means and prediction
# intervals
finalForecast <- cbind(sapply(adamPoolBJForecasts, "[[", "mean") %*%
adamsICWeights, sapply(adamPoolBJForecasts, "[[", "lower") %*%
adamsICWeights, sapply(adamPoolBJForecasts, "[[", "upper") %*%
adamsICWeights)
# Give the appropriate names
colnames(finalForecast) <- c("Mean", "Lower bound (2.5%)", "Upper bound (97.5%)")
# Transform the table in the ts format (for convenience)
finalForecast <- ts(finalForecast, start = start(adamPoolBJForecasts[[i]]$mean))
finalForecast
#> Time Series:
#> Start = 12
#> End = 21
#> Frequency = 1
#> Mean Lower bound (2.5%) Upper bound (97.5%)
#> 12 20727 11290 30164
#> 13 20727 7381 34072
#> 14 20727 4382 37072
#> 15 20727 1853 39600
#> 16 20727 -374 41828
#> 17 20727 -2388 43842
#> 18 20727 -4241 45694
#> 19 20727 -5964 47418
#> 20 20727 -7583 49037
#> 21 20727 -9115 50569
graphmaker(df1$y, finalForecast[, 1], lower = finalForecast[,
2], upper = finalForecast[, 3], level = 0.95)
plot(forecast(forecastHybrid::hybridModel(df1$y, models = "aen",
weights = "equal", cvHorizon = 8, num.cores = 4), h = 5))
plot(forecast(forecastHybrid::hybridModel(df1$y, models = "fnst",
weights = "equal", errorMethod = "RMSE")))
oesModel <- oes(df1$y, model = "YYY", occurrence = "auto")
y0 <- stan_sarima(df1$y, refresh = 0, verbose = FALSE, open_progress = FALSE)
autoplot(forecast(y0, 5, 0.99), "red") + ggplot2::theme_bw()
#> Error in tail.data.frame(data, include): invalid 'n' - must be numeric, possibly NA.
df1$month <- lubridate::month(df1$ds)
gam1 <- mgcv::gam(Sales ~ s(month, bs = "cr", k = 12), data = df1,
family = gaussian, correlation = SARIMA(form = ~month, p = 1),
method = "REML") |>
mgcv::plot.gam(lwd = 3, lty = 1, col = "#d46c5b")
ts_plot(df1, title = "US Monthly Natural Gas Consumption", Ytitle = "Billion Cubic Feet")
months <- c("2022-01-01", "2022-03-01", "2022-06-01")
ubereats <- c(7327.55, 4653.53, 4833.21)
doordash <- c(1304.54, 2000.35, 1643.58)
grubhub <- c(1199.85, 941.68, 623.27)
total <- c(7222.85, 7464.68, 7100.06)
df <- data.frame(months, ubereats, doordash, grubhub, total)
df$months <- as.Date(df$months)
ts_plot(df, title = "US Monthly Natural Gas Consumption", Ytitle = "Billion Cubic Feet")
df$total <- ts(df$total)
plot(greybox::forecast(adam(df$total, h = 5, holdout = TRUE,
ic = "AICc", regressors = "select")))
#> Error in h(simpleError(msg, call)): error in evaluating the argument 'x' in selecting a method for function 'plot': The number of in-sample observations is not positive. Cannot do anything.
m <- prophet(df, growth = "linear", yearly.seasonality = "auto")
#> Error in fit.prophet(m, df, ...): Dataframe must have columns 'ds' and 'y' with the dates and values respectively.
future <- make_future_dataframe(m, periods = 60, freq = "months",
include_history = TRUE)
#> Error in eval(expr, envir, enclos): object 'm' not found
forecast <- predict(m, future)
#> Error in eval(expr, envir, enclos): object 'm' not found
plot(m, forecast) + theme_bw()
#> Error in h(simpleError(msg, call)): error in evaluating the argument 'x' in selecting a method for function 'plot': object 'm' not found
# Plotting actual vs. fitted and forecasted
test_forecast(actual = df1$y, forecast.obj = fc, test = test$y)
#> Error in `recycle_columns()`:
#> ! Tibble columns must have compatible sizes.
#> • Size 21: Column `x`.
#> • Size 22: Columns `y` and `text`.
#> ℹ Only values of size one are recycled.
plot(fc)
import delimited "/Users/zad/Dropbox/LessLikely/ts.csv", clear
#> (encoding automatically selected: ISO-8859-1)
#> (5 vars, 21 obs)
#>
#>
#> N Child processes: 8
#> Stata dir: /Applications/Stata/StataBE.app/Contents/MacOS/stata-be
#>
#>
#> Time variable: t, 1 to 21
#> Delta: 1 unit
#>
#>
#>
#>
#> Dickey–Fuller test for unit root Number of obs = 20
#> Variable: sales Number of lags = 0
#>
#> H0: Random walk with or without drift
#>
#> Dickey–Fuller
#> Test -------- critical value ---------
#> statistic 1% 5% 10%
#> --------------------------------------------------------------
#> Z(t) -3.069 -4.380 -3.600 -3.240
#> --------------------------------------------------------------
#> MacKinnon approximate p-value for Z(t) = 0.1137.
#>
#> Regression table
#> ------------------------------------------------------------------------------
#> D.sales | Coefficient Std. err. t P>|t| [95% conf. interval]
#> -------------+----------------------------------------------------------------
#> sales |
#> L1. | -.5443834 .177365 -3.07 0.007 -.9185909 -.1701758
#> |
#> _trend | 113.3635 213.0871 0.53 0.602 -336.211 562.9381
#> _cons | 10627.12 2872.968 3.70 0.002 4565.683 16688.55
#> ------------------------------------------------------------------------------
#>
#>
#>
#>
#> (setting optimization to BHHH)
#> Iteration 0: log likelihood = -200.56293
#> Iteration 1: log likelihood = -199.59002
#> Iteration 2: log likelihood = -199.0124
#> Iteration 3: log likelihood = -198.71266
#> Iteration 4: log likelihood = -198.61803
#> (switching optimization to BFGS)
#> Iteration 5: log likelihood = -198.55245
#> Iteration 6: log likelihood = -198.4958
#> Iteration 7: log likelihood = -198.4736
#> Iteration 8: log likelihood = -198.47357
#> Iteration 9: log likelihood = -198.47278
#> Iteration 10: log likelihood = -198.47278
#>
#> ARIMA regression
#>
#> Sample: 2 thru 21 Number of obs = 20
#> Wald chi2(2) = 1.08
#> Log likelihood = -198.4728 Prob > chi2 = 0.5825
#>
#> ------------------------------------------------------------------------------
#> | OPG
#> D.sales | Coefficient std. err. z P>|z| [95% conf. interval]
#> -------------+----------------------------------------------------------------
#> sales |
#> _cons | 942.5678 1308.584 0.72 0.471 -1622.21 3507.346
#> -------------+----------------------------------------------------------------
#> ARMA |
#> ar |
#> L1. | -.2851484 1.365128 -0.21 0.835 -2.96075 2.390453
#> |
#> ma |
#> L1. | -.0079803 1.389017 -0.01 0.995 -2.730404 2.714444
#> -------------+----------------------------------------------------------------
#> /sigma | 4927.009 1205.311 4.09 0.000 2564.642 7289.375
#> ------------------------------------------------------------------------------
#> Note: The test of the variance against zero is one sided, and the two-sided
#> confidence interval is truncated at zero.
#>
#>
#> Akaike's information criterion and Bayesian information criterion
#>
#> -----------------------------------------------------------------------------
#> Model | N ll(null) ll(model) df AIC BIC
#> -------------+---------------------------------------------------------------
#> . | 20 . -198.4728 4 404.9456 408.9285
#> -----------------------------------------------------------------------------
#> Note: BIC uses N = number of observations. See [R] BIC note.
#>
#>
#> (setting optimization to BHHH)
#> Iteration 0: log likelihood = -212.32417
#> Iteration 1: log likelihood = -210.34653
#> Iteration 2: log likelihood = -209.35975
#> Iteration 3: log likelihood = -209.30035
#> Iteration 4: log likelihood = -209.2976
#> (switching optimization to BFGS)
#> Iteration 5: log likelihood = -209.29678
#> Iteration 6: log likelihood = -209.2963
#> Iteration 7: log likelihood = -209.29617
#> Iteration 8: log likelihood = -209.29616
#>
#> ARIMA regression
#>
#> Sample: 1 thru 21 Number of obs = 21
#> Wald chi2(1) = 40.00
#> Log likelihood = -209.2962 Prob > chi2 = 0.0000
#>
#> ------------------------------------------------------------------------------
#> | OPG
#> sales | Coefficient std. err. z P>|z| [95% conf. interval]
#> -------------+----------------------------------------------------------------
#> sales |
#> _cons | 17540.1 3291.584 5.33 0.000 11088.72 23991.49
#> -------------+----------------------------------------------------------------
#> ARMA |
#> ar |
#> L1. | .7741051 .1223945 6.32 0.000 .5342164 1.013994
#> -------------+----------------------------------------------------------------
#> /sigma | 5043.199 718.8693 7.02 0.000 3634.241 6452.157
#> ------------------------------------------------------------------------------
#> Note: The test of the variance against zero is one sided, and the two-sided
#> confidence interval is truncated at zero.
#>
#>
#> Akaike's information criterion and Bayesian information criterion
#>
#> -----------------------------------------------------------------------------
#> Model | N ll(null) ll(model) df AIC BIC
#> -------------+---------------------------------------------------------------
#> . | 21 . -209.2962 3 424.5923 427.7259
#> -----------------------------------------------------------------------------
#> Note: BIC uses N = number of observations. See [R] BIC note.
#>
#>
#> request ignored because of batch mode
#>
#>
#>
#>
#> file /Users/zad/Dropbox/LessLikely/content/post/statistics/forecastedsales.png saved as PNG
#> format
Python
from pandas import DataFrame
import statsmodels.api as sm
import matplotlib as plot
Stock_Market = {'Year': [2017,2017,2017,2017,2017,
2017,2017,2017,2017,2017,
2017,2017,2016,2016,2016,
2016,2016,2016,2016,2016,
2016,2016,2016,2016],
'Month': [12, 11,10,9,8,7,6,5,4,
3,2,1,12,11,10,9,8,7,6,
5,4,3,2,1],
'Interest_Rate':[2.75,2.5,2.5,2.5,2.5,2.5,
2.5,2.25,2.25,2.25,2,2,2,1.75,1.75,
1.75,1.75,1.75,1.75,1.75,1.75,1.75,1.75,1.75],
'Unemployment_Rate':[5.3,5.3,5.3,5.3,5.4,5.6,
5.5,5.5,5.5,5.6,5.7,5.9,6,5.9,5.8,6.1,
6.2,6.1,6.1,6.1,5.9,6.2,6.2,6.1],
'Stock_Index_Price': [1464,1394,1357,1293,1256,1254,1234,1195,1159,1167,1130,
1075,1047,965,943,958,971,949,884,866,876,822,704,719]
}
df = DataFrame(Stock_Market,columns=['Year','Month','Interest_Rate',
'Unemployment_Rate','Stock_Index_Price'])
X = df[['Interest_Rate','Unemployment_Rate']]
# here we have 2 variables for the multiple linear regression. If you just want to use one variable for simple linear regression, then use X = df['Interest_Rate'] for example
Y = df['Stock_Index_Price']
X = sm.add_constant(X) # adding a constant
model = sm.OLS(Y, X).fit()
predictions = model.predict(X)
print_model = model.summary()
print(print_model)
#> OLS Regression Results
#> ==============================================================================
#> Dep. Variable: Stock_Index_Price R-squared: 0.898
#> Model: OLS Adj. R-squared: 0.888
#> Method: Least Squares F-statistic: 92.07
#> Date: Tue, 09 Jan 2024 Prob (F-statistic): 4.04e-11
#> Time: 19:22:23 Log-Likelihood: -134.61
#> No. Observations: 24 AIC: 275.2
#> Df Residuals: 21 BIC: 278.8
#> Df Model: 2
#> Covariance Type: nonrobust
#> =====================================================================================
#> coef std err t P>|t| [0.025 0.975]
#> -------------------------------------------------------------------------------------
#> const 1798.4040 899.248 2.000 0.059 -71.685 3668.493
#> Interest_Rate 345.5401 111.367 3.103 0.005 113.940 577.140
#> Unemployment_Rate -250.1466 117.950 -2.121 0.046 -495.437 -4.856
#> ==============================================================================
#> Omnibus: 2.691 Durbin-Watson: 0.530
#> Prob(Omnibus): 0.260 Jarque-Bera (JB): 1.551
#> Skew: -0.612 Prob(JB): 0.461
#> Kurtosis: 3.226 Cond. No. 394.
#> ==============================================================================
#>
#> Notes:
#> [1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
R
fit <- glm(mpg ~ cyl + disp, mtcars, family = gaussian())
# show the theoretical model
equatiomatic::extract_eq(fit)
\[ E( \operatorname{mpg} ) = \alpha + \beta_{1}(\operatorname{cyl}) + \beta_{2}(\operatorname{disp}) \]
Stata
sysuse auto2, clear
parallel initialize 8, f
mfp: glm price mpg
twoway (fpfitci price mpg, estcmd(glm) fcolor(dkorange%20) alcolor(%40)) || scatter price mpg, mcolor(dkorange) scale(0.75)
graph export "mfp.png", replace
#> . sysuse auto2, clear
#> (1978 automobile data)
#>
#> . parallel initialize 8, f
#> N Child processes: 8
#> Stata dir: /Applications/Stata/StataBE.app/Contents/MacOS/stata-be
#>
#> . mfp: glm price mpg
#>
#> Deviance for model with all terms untransformed = 1373.079, 74 observations
#>
#> Variable Model (vs.) Deviance Dev diff. P Powers (vs.)
#> ----------------------------------------------------------------------
#> mpg Lin. FP2 1373.079 19.565 0.000+ 1 -2 -2
#> FP1 1356.927 3.413 0.182 -2
#> Final 1356.927 -2
#>
#>
#> Transformations of covariates:
#>
#> -> gen double Impg__1 = X^-2-.2204707671 if e(sample)
#> (where: X = mpg/10)
#>
#> Final multivariable fractional polynomial model for price
#> --------------------------------------------------------------------
#> Variable | -----Initial----- -----Final-----
#> | df Select Alpha Status df Powers
#> -------------+------------------------------------------------------
#> mpg | 4 1.0000 0.0500 in 2 -2
#> --------------------------------------------------------------------
#>
#> Generalized linear models Number of obs = 74
#> Optimization : ML Residual df = 72
#> Scale parameter = 5533697
#> Deviance = 398426217.4 (1/df) Deviance = 5533697
#> Pearson = 398426217.4 (1/df) Pearson = 5533697
#>
#> Variance function: V(u) = 1 [Gaussian]
#> Link function : g(u) = u [Identity]
#>
#> AIC = 18.3909
#> Log likelihood = -678.4632599 BIC = 3.98e+08
#>
#> ------------------------------------------------------------------------------
#> | OIM
#> price | Coefficient std. err. z P>|z| [95% conf. interval]
#> -------------+----------------------------------------------------------------
#> Impg__1 | 13163.85 2013.016 6.54 0.000 9218.41 17109.29
#> _cons | 5538.395 289.7737 19.11 0.000 4970.449 6106.341
#> ------------------------------------------------------------------------------
#> Deviance = 1356.927.
#>
#> . twoway (fpfitci price mpg, estcmd(glm) fcolor(dkorange%20) alcolor(%40)) || scatter price mp
#> > g, mcolor(dkorange) scale(0.75)
#>
#> . graph export "mfp.png", replace
#> file /Users/zad/Dropbox/LessLikely/content/post/statistics/mfp.png saved as PNG format
#>
#> .
clear
set obs 100
/**
Generate variables from a normal distribution like before
*/
generate x = rnormal(0, 1)
generate y = rnormal(0, 1)
/**
We set up our model here
*/
parallel initialize 8, f
bayesmh y x, likelihood(normal({var})) prior({var}, normal(0, 10)) ///
prior({y:}, normal(0, 10)) rseed(1031) saving(coutput_pred, replace) mcmcsize(1000)
/**
We use the bayespredict command to make predictions from the model
*/
bayespredict (mean:@mean({_resid})) (var:@variance({_resid})), ///
rseed(1031) saving(coutput_pred, replace)
/**
Then we calculate the posterior predictive P-values
*/
bayesstats ppvalues {mean} using coutput_pred
#> . clear
#>
#> . set obs 100
#> Number of observations (_N) was 0, now 100.
#>
#> . /**
#> > Generate variables from a normal distribution like before
#> > */
#> . generate x = rnormal(0, 1)
#>
#> . generate y = rnormal(0, 1)
#>
#> . /**
#> > We set up our model here
#> >
#> > */
#> . parallel initialize 8, f
#> N Child processes: 8
#> Stata dir: /Applications/Stata/StataBE.app/Contents/MacOS/stata-be
#>
#> . bayesmh y x, likelihood(normal({var})) prior({var}, normal(0, 10)) ///
#> > prior({y:}, normal(0, 10)) rseed(1031) saving(coutput_pred, replace) mcmcsize(1000)
#>
#> Burn-in ...
#> Simulation ...
#>
#> Model summary
#> ------------------------------------------------------------------------------
#> Likelihood:
#> y ~ normal(xb_y,{var})
#>
#> Priors:
#> {y:x _cons} ~ normal(0,10) (1)
#> {var} ~ normal(0,10)
#> ------------------------------------------------------------------------------
#> (1) Parameters are elements of the linear form xb_y.
#>
#> Bayesian normal regression MCMC iterations = 3,500
#> Random-walk Metropolis–Hastings sampling Burn-in = 2,500
#> MCMC sample size = 1,000
#> Number of obs = 100
#> Acceptance rate = .2068
#> Efficiency: min = .03878
#> avg = .07757
#> Log marginal-likelihood = -149.68351 max = .1317
#>
#> ------------------------------------------------------------------------------
#> | Equal-tailed
#> | Mean Std. dev. MCSE Median [95% cred. interval]
#> -------------+----------------------------------------------------------------
#> y |
#> x | -.0758396 .097915 .008532 -.0704775 -.2600037 .1054718
#> _cons | .0238076 .1107038 .014035 .0326669 -.1793756 .2293247
#> -------------+----------------------------------------------------------------
#> var | .9773565 .1313659 .021096 .9384637 .7882847 1.323255
#> ------------------------------------------------------------------------------
#>
#> file coutput_pred.dta saved.
#>
#> . /**
#> > We use the bayespredict command to make predictions from the model
#> > */
#> . bayespredict (mean:@mean({_resid})) (var:@variance({_resid})), ///
#> > rseed(1031) saving(coutput_pred, replace)
#>
#> Computing predictions ...
#>
#> file coutput_pred.dta saved.
#> file coutput_pred.ster saved.
#>
#> . /**
#> > Then we calculate the posterior predictive P-values
#> > */
#> . bayesstats ppvalues {mean} using coutput_pred
#>
#> Posterior predictive summary MCMC sample size = 1,000
#>
#> -----------------------------------------------------------
#> T | Mean Std. dev. E(T_obs) P(T>=T_obs)
#> -------------+---------------------------------------------
#> mean | .0004223 .0957513 .008651 .495
#> -----------------------------------------------------------
#> Note: P(T>=T_obs) close to 0 or 1 indicates lack of fit.
#>
#> .
library(lme4)
library(simr)
# Toy model
fm = lmer(y ~ x + (x | g), data = simdata)
# Extend sample size of `g`
fm_extended_g = extend(fm, along = 'g', n = 4)
# 4 levels of g
pwcurve_4g = powerCurve(fm_extended_g, fixed('x'), along = 'g', breaks = 4,
nsim = 50, seed = 123,
# No progress bar
progress = FALSE)
# 6 levels of g
# Create a destination object using any of the power curves above.
all_pwcurve = pwcurve_4g
# Combine results
all_pwcurve$ps = c(pwcurve_4g$ps[1])
# Combine the different numbers of levels.
all_pwcurve$xval = c(pwcurve_4g$nlevels)
print(all_pwcurve)
#> Power for predictor 'x', (95% confidence interval),
#> by number of levels in g:
#> 4: 44.00% (29.99, 58.75) - 40 rows
#>
#> Time elapsed: 0 h 0 m 20 s
plot(all_pwcurve, xlab = 'Levels of g')
Julia
Pkg.add("Plots")
using Plots
gr()
#> Plots.GRBackend()
Plots.GRBackend()
#> Plots.GRBackend()
plot(Plots.fakedata(50,5),w=3)
#> Plot{Plots.GRBackend() n=5}
png("sample.png")
Computational Environments
Overall Platforms
sessioninfo::session_info(info = c("platform", "external"))
#> Error in info != "auto" && info != "all": 'length = 2' in coercion to 'logical(1)'
R
Packages
sessioninfo::session_info(info = "packages")
#> ═ Session info ═════════════════════════════════════════════════════════════════════════════════════════════════════════════════
#> ─ Packages ─────────────────────────────────────────────────────────────────────────────────────────────────────────────────────
#> package * version date (UTC) lib source
#> abind 1.4-5 2016-07-21 [2] CRAN (R 4.3.0)
#> ADGofTest 0.3 2011-12-28 [2] CRAN (R 4.3.0)
#> Amelia * 1.8.1 2022-11-19 [2] CRAN (R 4.3.0)
#> anytime 0.3.9 2020-08-27 [2] CRAN (R 4.3.0)
#> arm 1.13-1 2022-08-28 [2] CRAN (R 4.3.0)
#> arrayhelpers 1.1-0 2020-02-04 [2] CRAN (R 4.3.0)
#> askpass 1.2.0 2023-09-03 [2] CRAN (R 4.3.0)
#> assertthat 0.2.1 2019-03-21 [2] CRAN (R 4.3.0)
#> astsa * 2.0 2023-01-09 [2] CRAN (R 4.3.0)
#> backports 1.4.1 2021-12-13 [2] CRAN (R 4.3.0)
#> base64enc 0.1-3 2015-07-28 [2] CRAN (R 4.3.0)
#> bayesforecast * 1.0.1 2021-06-17 [2] CRAN (R 4.3.0)
#> bayesplot * 1.10.0 2022-11-16 [2] CRAN (R 4.3.0)
#> bcaboot 0.2-3 2021-05-09 [2] CRAN (R 4.3.0)
#> benchmarkme 1.0.8 2022-06-12 [2] CRAN (R 4.3.0)
#> benchmarkmeData 1.0.4 2020-04-23 [2] CRAN (R 4.3.0)
#> binom 1.1-1.1 2022-05-02 [2] CRAN (R 4.3.0)
#> bitops 1.0-7 2021-04-24 [2] CRAN (R 4.3.0)
#> blogdown * 1.18.1 2023-07-21 [1] Github (rstudio/blogdown@6ab3a2b)
#> bookdown 0.37 2023-12-01 [2] CRAN (R 4.3.1)
#> boot * 1.3-28.1 2022-11-22 [2] CRAN (R 4.3.2)
#> bootImpute * 1.2.1 2023-06-01 [2] CRAN (R 4.3.0)
#> bridgesampling 1.1-2 2021-04-16 [2] CRAN (R 4.3.0)
#> brms * 2.20.4 2023-09-25 [1] CRAN (R 4.3.1)
#> Brobdingnag 1.2-9 2022-10-19 [2] CRAN (R 4.3.0)
#> broom * 1.0.5 2023-06-09 [2] CRAN (R 4.3.0)
#> broom.mixed * 0.2.9.4 2022-04-17 [2] CRAN (R 4.3.0)
#> bslib 0.6.1 2023-11-28 [2] CRAN (R 4.3.1)
#> cachem 1.0.8 2023-05-01 [2] CRAN (R 4.3.0)
#> Cairo * 1.6-2 2023-11-28 [2] CRAN (R 4.3.1)
#> callr 3.7.3 2022-11-02 [2] CRAN (R 4.3.0)
#> car * 3.1-2 2023-03-30 [2] CRAN (R 4.3.0)
#> carData * 3.0-5 2022-01-06 [2] CRAN (R 4.3.0)
#> caTools 1.18.2 2021-03-28 [2] CRAN (R 4.3.0)
#> checkmate * 2.3.1 2023-12-04 [2] CRAN (R 4.3.1)
#> class 7.3-22 2023-05-03 [2] CRAN (R 4.3.2)
#> cli 3.6.2 2023-12-11 [1] CRAN (R 4.3.1)
#> clipr 0.8.0 2022-02-22 [2] CRAN (R 4.3.0)
#> clock 0.7.0 2023-05-15 [2] CRAN (R 4.3.0)
#> cluster 2.1.6 2023-12-01 [2] CRAN (R 4.3.1)
#> cmdstanr * 0.5.3 2023-06-29 [2] Github (stan-dev/cmdstanr@dbf41cd)
#> coda * 0.19-4 2020-09-30 [2] CRAN (R 4.3.0)
#> codetools 0.2-19 2023-02-01 [2] CRAN (R 4.3.2)
#> colorspace * 2.1-0 2023-01-23 [2] CRAN (R 4.3.0)
#> colourpicker 1.3.0 2023-08-21 [2] CRAN (R 4.3.0)
#> concurve * 2.8.0 2023-05-02 [2] local
#> copula 1.1-3 2023-12-07 [2] CRAN (R 4.3.1)
#> cowplot * 1.1.2 2023-12-15 [2] CRAN (R 4.3.1)
#> crayon 1.5.2 2022-09-29 [2] CRAN (R 4.3.0)
#> crosstalk 1.2.1 2023-11-23 [2] CRAN (R 4.3.1)
#> crul 1.4.0 2023-05-17 [2] CRAN (R 4.3.0)
#> curl 5.2.0 2023-12-08 [2] CRAN (R 4.3.1)
#> data.table 1.14.10 2023-12-08 [2] CRAN (R 4.3.1)
#> DBI 1.2.0 2023-12-21 [2] CRAN (R 4.3.1)
#> DEoptimR 1.1-3 2023-10-07 [2] CRAN (R 4.3.1)
#> desc 1.4.3 2023-12-10 [2] CRAN (R 4.3.2)
#> details 0.3.0 2022-03-27 [2] CRAN (R 4.3.0)
#> devtools 2.4.5 2022-10-11 [1] CRAN (R 4.3.0)
#> dials * 1.2.0 2023-04-03 [2] CRAN (R 4.3.0)
#> DiceDesign 1.10 2023-12-07 [2] CRAN (R 4.3.1)
#> digest 0.6.33 2023-07-07 [1] CRAN (R 4.3.0)
#> distr 2.9.2 2023-05-08 [2] CRAN (R 4.3.0)
#> distrEx 2.9.0 2022-11-15 [2] CRAN (R 4.3.0)
#> distributional 0.3.2 2023-03-22 [2] CRAN (R 4.3.0)
#> doParallel * 1.0.17 2022-02-07 [2] CRAN (R 4.3.0)
#> doRNG 1.8.6 2023-01-16 [2] CRAN (R 4.3.0)
#> dplyr * 1.1.4 2023-11-17 [2] CRAN (R 4.3.1)
#> DT 0.31 2023-12-09 [2] CRAN (R 4.3.1)
#> dygraphs 1.1.1.6 2018-07-11 [1] CRAN (R 4.3.0)
#> e1071 1.7-14 2023-12-06 [2] CRAN (R 4.3.1)
#> earth * 5.3.2 2023-01-26 [2] CRAN (R 4.3.0)
#> easypackages 0.1.0 2016-12-05 [2] CRAN (R 4.3.0)
#> ellipsis 0.3.2 2021-04-29 [2] CRAN (R 4.3.0)
#> emmeans 1.9.0 2023-12-18 [2] CRAN (R 4.3.1)
#> equatiomatic 0.3.1 2022-01-30 [2] CRAN (R 4.2.0)
#> estimability 1.4.1 2022-08-05 [2] CRAN (R 4.3.0)
#> evaluate 0.23 2023-11-01 [1] CRAN (R 4.3.2)
#> evd 2.3-6.1 2022-07-04 [2] CRAN (R 4.3.0)
#> extremevalues 2.3.3 2020-05-18 [2] CRAN (R 4.3.0)
#> fable * 0.3.3 2023-03-22 [2] CRAN (R 4.3.0)
#> fabletools * 0.3.4 2023-10-11 [2] CRAN (R 4.3.1)
#> fansi 1.0.6 2023-12-08 [2] CRAN (R 4.3.1)
#> farver 2.1.1 2022-07-06 [2] CRAN (R 4.3.0)
#> fastmap 1.1.1 2023-02-24 [2] CRAN (R 4.3.0)
#> flextable 0.9.4 2023-10-22 [2] CRAN (R 4.3.1)
#> fontBitstreamVera 0.1.1 2017-02-01 [2] CRAN (R 4.3.0)
#> fontLiberation 0.1.0 2016-10-15 [2] CRAN (R 4.3.0)
#> fontquiver 0.2.1 2017-02-01 [2] CRAN (R 4.3.0)
#> forcats * 1.0.0 2023-01-29 [2] CRAN (R 4.3.0)
#> foreach * 1.5.2 2022-02-02 [2] CRAN (R 4.3.0)
#> forecast * 8.21.1 2023-08-31 [2] CRAN (R 4.3.0)
#> forecastHybrid 5.0.19 2020-08-28 [2] CRAN (R 4.3.0)
#> foreign 0.8-86 2023-11-28 [2] CRAN (R 4.3.1)
#> formatR 1.14 2023-01-17 [2] CRAN (R 4.3.0)
#> Formula * 1.2-5 2023-02-24 [2] CRAN (R 4.3.0)
#> fracdiff 1.5-2 2022-10-31 [2] CRAN (R 4.3.0)
#> fs 1.6.3 2023-07-20 [2] CRAN (R 4.3.0)
#> furrr 0.3.1 2022-08-15 [2] CRAN (R 4.3.0)
#> future * 1.33.1 2023-12-22 [2] CRAN (R 4.3.2)
#> future.apply * 1.11.1 2023-12-21 [2] CRAN (R 4.3.1)
#> gamlss * 5.4-20 2023-10-04 [2] CRAN (R 4.3.1)
#> gamlss.data * 6.0-2 2021-11-07 [2] CRAN (R 4.3.0)
#> gamlss.dist * 6.1-1 2023-08-23 [2] CRAN (R 4.3.0)
#> gdtools 0.3.5 2023-12-09 [2] CRAN (R 4.3.1)
#> generics 0.1.3 2022-07-05 [2] CRAN (R 4.3.0)
#> gfonts 0.2.0 2023-01-08 [2] CRAN (R 4.3.0)
#> ggcorrplot * 0.1.4.1 2023-09-05 [2] CRAN (R 4.3.0)
#> ggdist 3.3.1 2023-11-27 [2] CRAN (R 4.3.1)
#> ggmice * 0.1.0 2023-08-07 [2] CRAN (R 4.3.0)
#> ggplot2 * 3.4.4 2023-10-12 [2] CRAN (R 4.3.1)
#> ggpubr 0.6.0 2023-02-10 [2] CRAN (R 4.3.0)
#> ggsignif 0.6.4 2022-10-13 [2] CRAN (R 4.3.0)
#> ggtext * 0.1.2 2022-09-16 [2] CRAN (R 4.3.0)
#> GJRM 0.2-6.4 2023-06-21 [2] CRAN (R 4.3.0)
#> glmnet * 4.1-8 2023-08-22 [2] CRAN (R 4.3.0)
#> globals 0.16.2 2022-11-21 [2] CRAN (R 4.3.0)
#> glue 1.6.2 2022-02-24 [1] CRAN (R 4.3.0)
#> gmp 0.7-3 2023-11-28 [2] CRAN (R 4.3.1)
#> gower 1.0.1 2022-12-22 [2] CRAN (R 4.3.0)
#> GPfit 1.0-8 2019-02-08 [2] CRAN (R 4.3.0)
#> greybox * 2.0.0 2023-09-16 [2] CRAN (R 4.3.0)
#> gridExtra 2.3 2017-09-09 [2] CRAN (R 4.3.0)
#> gridtext 0.1.5 2022-09-16 [2] CRAN (R 4.3.0)
#> gsl 2.1-8 2023-01-24 [2] CRAN (R 4.3.0)
#> gtable 0.3.4 2023-08-21 [2] CRAN (R 4.3.0)
#> gtools 3.9.5 2023-11-20 [2] CRAN (R 4.3.1)
#> gWidgets2 1.0-9 2022-01-10 [2] CRAN (R 4.3.0)
#> gWidgets2tcltk 1.0-8 2022-02-16 [2] CRAN (R 4.3.0)
#> hardhat 1.3.0 2023-03-30 [2] CRAN (R 4.3.0)
#> here * 1.0.1 2020-12-13 [1] CRAN (R 4.3.2)
#> highr 0.10.1 2023-03-24 [2] https://yihui.r-universe.dev (R 4.3.0)
#> Hmisc * 5.1-1 2023-09-12 [2] CRAN (R 4.3.0)
#> hms 1.1.3 2023-03-21 [2] CRAN (R 4.3.0)
#> htmlTable 2.4.2 2023-10-29 [2] CRAN (R 4.3.1)
#> htmltools * 0.5.7 2023-11-03 [2] CRAN (R 4.3.1)
#> htmlwidgets 1.6.4 2023-12-06 [2] CRAN (R 4.3.1)
#> httpcode 0.3.0 2020-04-10 [2] CRAN (R 4.3.0)
#> httpuv 1.6.13 2023-12-06 [2] CRAN (R 4.3.1)
#> httr 1.4.7 2023-08-15 [2] CRAN (R 4.3.0)
#> igraph 1.6.0 2023-12-11 [2] CRAN (R 4.3.1)
#> ImputeRobust * 1.3-1 2018-11-30 [2] CRAN (R 4.3.0)
#> infer * 1.0.5 2023-09-06 [2] CRAN (R 4.3.0)
#> inline 0.3.19 2021-05-31 [2] CRAN (R 4.3.0)
#> insight 0.19.7 2023-11-26 [1] CRAN (R 4.3.1)
#> ipred 0.9-14 2023-03-09 [2] CRAN (R 4.3.0)
#> ismev 1.42 2018-05-10 [2] CRAN (R 4.3.0)
#> iterators * 1.0.14 2022-02-05 [2] CRAN (R 4.3.0)
#> itertools 0.1-3 2014-03-12 [2] CRAN (R 4.3.0)
#> janitor 2.2.0 2023-02-02 [2] CRAN (R 4.3.0)
#> jomo 2.7-6 2023-04-15 [2] CRAN (R 4.3.0)
#> jquerylib 0.1.4 2021-04-26 [2] CRAN (R 4.3.0)
#> jsonlite 1.8.8 2023-12-04 [2] CRAN (R 4.3.1)
#> JuliaCall * 0.17.5 2022-09-08 [2] CRAN (R 4.3.0)
#> kableExtra * 1.3.4 2021-02-20 [2] CRAN (R 4.3.0)
#> katex * 1.4.1 2022-11-28 [2] CRAN (R 4.3.0)
#> keras * 2.13.0 2023-08-15 [2] CRAN (R 4.3.0)
#> km.ci 0.5-6 2022-04-06 [2] CRAN (R 4.3.0)
#> KMsurv 0.1-5 2012-12-03 [2] CRAN (R 4.3.0)
#> knitr * 1.45 2023-10-30 [2] CRAN (R 4.3.1)
#> labeling 0.4.3 2023-08-29 [2] CRAN (R 4.3.0)
#> laeken 0.5.2 2021-10-06 [2] CRAN (R 4.3.0)
#> later 1.3.2 2023-12-06 [2] CRAN (R 4.3.1)
#> latex2exp * 0.9.6 2022-11-28 [2] CRAN (R 4.3.0)
#> lattice * 0.22-5 2023-10-24 [2] CRAN (R 4.3.1)
#> lava 1.7.3 2023-11-04 [2] CRAN (R 4.3.0)
#> lazyeval 0.2.2 2019-03-15 [2] CRAN (R 4.3.0)
#> lhs 1.1.6 2022-12-17 [2] CRAN (R 4.3.0)
#> lifecycle 1.0.4 2023-11-07 [1] CRAN (R 4.3.1)
#> listenv 0.9.0 2022-12-16 [2] CRAN (R 4.3.0)
#> lme4 * 1.1-35.1 2023-11-05 [2] CRAN (R 4.3.1)
#> lmtest 0.9-40 2022-03-21 [2] CRAN (R 4.3.0)
#> loo * 2.6.0 2023-03-31 [1] CRAN (R 4.3.0)
#> lubridate * 1.9.3 2023-09-27 [2] CRAN (R 4.3.1)
#> magic 1.6-1 2022-11-16 [2] CRAN (R 4.3.0)
#> magick 2.8.2 2023-12-20 [2] CRAN (R 4.3.1)
#> magrittr * 2.0.3 2022-03-30 [1] CRAN (R 4.3.0)
#> markdown 1.12 2023-12-06 [2] CRAN (R 4.3.1)
#> MASS * 7.3-60 2023-05-04 [2] CRAN (R 4.3.2)
#> mathjaxr 1.6-0 2022-02-28 [2] CRAN (R 4.3.0)
#> Matrix * 1.6-4 2023-11-30 [2] CRAN (R 4.3.1)
#> MatrixModels 0.5-3 2023-11-06 [2] CRAN (R 4.3.0)
#> matrixStats 1.2.0 2023-12-11 [2] CRAN (R 4.3.1)
#> maxLik 1.5-2 2021-07-26 [2] CRAN (R 4.3.0)
#> mcmc 0.9-8 2023-11-16 [2] CRAN (R 4.3.1)
#> MCMCpack * 1.6-3 2022-04-13 [2] CRAN (R 4.3.0)
#> memoise 2.0.1 2021-11-26 [2] CRAN (R 4.3.0)
#> memuse 4.2-3 2023-01-24 [2] CRAN (R 4.3.0)
#> metadat 1.2-0 2022-04-06 [2] CRAN (R 4.3.0)
#> metafor 4.4-0 2023-09-27 [2] CRAN (R 4.3.1)
#> mgcv * 1.9-1 2023-12-21 [2] CRAN (R 4.3.1)
#> mi * 1.1 2022-06-06 [2] CRAN (R 4.3.0)
#> mice * 3.16.0 2023-06-05 [2] CRAN (R 4.3.0)
#> mice.mcerror * 0.0.0-9000 2022-05-13 [2] Github (ellessenne/mice.mcerror@327b513)
#> miceadds * 3.16-18 2023-01-06 [2] CRAN (R 4.3.0)
#> miceFast * 0.8.2 2022-11-17 [2] CRAN (R 4.3.0)
#> miceMNAR * 1.0.2 2018-08-27 [2] CRAN (R 4.2.0)
#> mime 0.12 2021-09-28 [2] CRAN (R 4.3.0)
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#> ────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────
Stata Environment
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#> January 9,2024 7:23 pm
#>
#>
#> Stata/BE 17.0 for Mac (Apple Silicon)
#> Revision 19 Dec 2023
#> Copyright 1985-2021 StataCorp LLC
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#> Total physical memory: 24.00 GB
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#> Stata license: Single-user perpetual
#> Serial number: 301706317553
#> Licensed to: Zad Rafi
#> AMG
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