Test: data_thirst

Load data

data(
  thirst,
  package = "jeksterslabRdatarepo"
)

Model

\[\begin{equation} Y_i = \delta_Y + \tau^{ \prime } X_i + \beta M_i + \varepsilon_{ Y_{ i } }, \\ \enspace \text{ where } \enspace \boldsymbol{ \varepsilon_{ Y_{ i } } } \sim \mathcal{ N } \left( \mu_{\varepsilon_{Y_{i}}} = 0, \sigma^{ 2 }_{ \varepsilon_{ Y_{ i } } } \mathrm{ I } \right) \end{equation}\]

\[\begin{equation} M_i = \delta_M + \alpha X_i + \varepsilon_{ M_i }, \\ \enspace \text{where} \enspace \boldsymbol{ \varepsilon_{ M_i } } \sim \mathcal{ N } \left( \mu_{ \varepsilon_{ M_{ i } } } = 0, \sigma^2_{ \varepsilon_{ M_i } } \mathrm{ I } \right) \end{equation}\]

Data

Variables
Variable	Description	Notation
`temp`	Room temperature in degrees Fahrenheit.	\(X\)
`thirst`	Self-reported thirst at the end of a 2-hour period.	\(M\)
`water`	Water consumed during the last 2 hours in deciliters.	\(Y\)

Mean structure

Estimated mean of \(X\) and regression intercepts
Variable	Description	Notation	Value
`muhatX`	Estimated mean of \(X\).	\(\hat{\mu}_X\)	70.18000
`deltahatM`	Estimated intercept of \(M\).	\(\hat{\delta}_M\)	-20.70243
`deltahatY`	Estimated intercept of \(Y\).	\(\hat{\delta}_Y\)	-12.71288

Covariance structure

Estimated regression slopes
Variable	Description	Notation	Value
`alphahat`	Estimated regression slope of path from \(X\) to \(M\).	\(\hat{\alpha}\)	0.3385926
`tauprimehat`	Estimated regression slope of path from \(X\) to \(Y\).	\(\hat{\tau}^{\prime}\)	0.2076475
`betahat`	Estimated regression slope of path from \(M\) to \(Y\).	\(\hat{\beta}\)	0.4510391
`alphahatbetahat`	Estimated indirect effect.	\(\hat{\alpha} \hat{\beta}\)	0.1527185

Estimated variance of \(X\) and error variances
Variable	Description	Notation	Value
`sigma2hatX`	Estimated variance of \(X\).	\(\hat{\sigma}^2_X\)	1.2934694
`sigma2hatepsilonhatM`	Estimated error variance of \(\hat{\varepsilon}_M\).	\(\hat{\sigma}^2_{\hat{\varepsilon}_{M}}\)	0.9490376
`sigma2hatepsilonhatY`	Estimated error variance of \(\hat{\varepsilon}_Y\).	\(\hat{\sigma}^2_{\hat{\varepsilon}_{Y}}\)	0.9706797

Fitted model-implied variance-covariance matrix

\(\boldsymbol{\hat{\mu}} \left( \boldsymbol{\hat{\theta}} \right)\) (`muhatthetahat`)
	x
X	70.18
M	3.06
Y	3.24

Fitted model-implied mean vector

\(\boldsymbol{\hat{\Sigma}} \left( \boldsymbol{\hat{\theta}} \right)\) (`Sigmahatthetahat`)
	X	M	Y
X	1.2934694	0.4379592	0.4661224
M	0.4379592	1.0973273	0.5858786
Y	0.4661224	0.5858786	1.3317230

testthat

test_that("regression_coefficients", {
  expect_equivalent(
    round(
      c(
        -20.702430,
        0.338593,
        -12.712884,
        0.207648,
        0.451039
      ),
      digits = 2
    ),
    round(
      c(
        deltahatM,
        alphahat,
        deltahatY,
        tauprimehat,
        betahat
      ),
      digits = 2
    )
  )
})
#> Test passed 🥳

Ivan Jacob Agaloos Pesigan

2020-12-31