Skip to main content
added 25 characters in body
Source Link
abc
  • 1.8k
  • 3
  • 19
  • 33

For the repeated measures design D.C.Montgomery in his "Design and Analysis of Experiments" book provides the mathematical / statistical (linear) model (with changes): $y_{ij} = \mu + \beta_j + \tau_i + \epsilon_{ij}$$y_{ij} = \mu + \beta_i + \tau_j + \epsilon_{ij}$, where $\beta$ is a parameter associated with the $j$$i$th subject, $\tau$ is the effect of the $i$$j$th treatment, and $\epsilon_{ij}$$\epsilon$ is the independent error.
In Weixing Song's document (page 2) it is stated that to check the model's assumptions we should operate with residuals calculated as (A): $$\hat\epsilon_{ij} = Y_{ij} - \bar Y_{i.} - \bar Y_{.j} + \bar Y.$$

The formula (B) on Wikipedia is $$\hat\epsilon_i = Y_i - \bar Y.$$

My question is:
what formula is used to correctly calculate residuals in the model describing a single-factor repeated measures design to check its assumptions (multivariate normality, homoscedasticity, sphericity, linearity, additivity)?

Thank you.

P.S.
E.Vonesh and V.M.Chinchilli in their "Linear and Nonlinear Models for the Analysis of Repeated Measurements" monograph state that the model for single-sample RM design may be written as $y_{i} = \mu + \epsilon_{i}$.

For the repeated measures design D.C.Montgomery in his "Design and Analysis of Experiments" book provides the mathematical / statistical (linear) model (with changes): $y_{ij} = \mu + \beta_j + \tau_i + \epsilon_{ij}$, where $\beta$ is a parameter associated with the $j$th subject, $\tau$ is the effect of the $i$th treatment, and $\epsilon_{ij}$ is the independent error.
In Weixing Song's document (page 2) it is stated that to check the model's assumptions we should operate with residuals calculated as (A): $$\hat\epsilon_{ij} = Y_{ij} - \bar Y_{i.} - \bar Y_{.j} + \bar Y.$$

The formula (B) on Wikipedia is $$\hat\epsilon_i = Y_i - \bar Y.$$

My question is:
what formula is used to correctly calculate residuals in the model describing a single-factor repeated measures design to check its assumptions (multivariate normality, homoscedasticity, sphericity, linearity, additivity)?

Thank you.

P.S.
E.Vonesh and V.M.Chinchilli in their "Linear and Nonlinear Models for the Analysis of Repeated Measurements" monograph state that the single-sample RM design may be written as $y_{i} = \mu + \epsilon_{i}$.

For the repeated measures design D.C.Montgomery in his "Design and Analysis of Experiments" book provides the mathematical / statistical (linear) model (with changes): $y_{ij} = \mu + \beta_i + \tau_j + \epsilon_{ij}$, where $\beta$ is a parameter associated with the $i$th subject, $\tau$ is the effect of the $j$th treatment, and $\epsilon$ is the independent error.
In Weixing Song's document it is stated that to check the model's assumptions we should operate with residuals calculated as (A): $$\hat\epsilon_{ij} = Y_{ij} - \bar Y_{i.} - \bar Y_{.j} + \bar Y.$$

The formula (B) on Wikipedia is $$\hat\epsilon_i = Y_i - \bar Y.$$

My question is:
what formula is used to correctly calculate residuals in the model describing a single-factor repeated measures design to check its assumptions (multivariate normality, homoscedasticity, sphericity, linearity, additivity)?

Thank you.

P.S.
E.Vonesh and V.M.Chinchilli in their "Linear and Nonlinear Models for the Analysis of Repeated Measurements" monograph state that the model for single-sample RM design may be written as $y_{i} = \mu + \epsilon_{i}$.

added 25 characters in body
Source Link
abc
  • 1.8k
  • 3
  • 19
  • 33

For the repeated measures design D.C.Montgomery in his "Design and Analysis of Experiments" book provides the mathematical / statistical (linear) model (with changes): $y_{ij} = \mu + \tau_i+ \beta_j + \epsilon_{ij}$$y_{ij} = \mu + \beta_j + \tau_i + \epsilon_{ij}$, where $\tau$ is the effect of the $i$th treatment, $\beta$ is a parameter associated with the $j$th subject, $\tau$ is the effect of the $i$th treatment, and $\epsilon_{ij}$ is the independent error.
In aWeixing Song's document (document, p.page 2) it is stated that to check the model's assumptions we should operate with residuals calculated as (A): $$\hat\epsilon_{ij} = Y_{ij} - \bar Y_{i.} - \bar Y_{.j} + \bar Y.$$

The formula (B) on Wikipedia is $$\hat\epsilon_i = Y_i - \bar Y.$$

My question is:
what formula is used to correctly calculate residuals in the model describing a single-factor repeated measures design to check its assumptions (multivariate normality, homoscedasticity, sphericity, linearity, additivity)?

Thank you.

pP.S.
E.Vonesh and V.M.Chinchilli in their "Linear and Nonlinear Models for the Analysis of Repeated Measurements" monograph state that the single-sample RM design may be written as $y_{i} = \mu + \epsilon_{i}$.

For the repeated measures design D.C.Montgomery in his "Design and Analysis of Experiments" book provides the mathematical / statistical (linear) model: $y_{ij} = \mu + \tau_i+ \beta_j + \epsilon_{ij}$, where $\tau$ is the effect of the $i$th treatment, $\beta$ is a parameter associated with the $j$th subject, and $\epsilon_{ij}$ is the independent error.
In a (document, p. 2) it is stated that to check the model's assumptions we should operate with residuals calculated as (A): $$\hat\epsilon_{ij} = Y_{ij} - \bar Y_{i.} - \bar Y_{.j} + \bar Y.$$

The formula (B) on Wikipedia is $$\hat\epsilon_i = Y_i - \bar Y.$$

My question is:
what formula is used to correctly calculate residuals in the model describing a single-factor repeated measures design to check its assumptions (multivariate normality, homoscedasticity, sphericity, linearity, additivity)?

Thank you.

p.S.
E.Vonesh and V.M.Chinchilli in their "Linear and Nonlinear Models for the Analysis of Repeated Measurements" monograph state that the single-sample RM design may be written as $y_{i} = \mu + \epsilon_{i}$.

For the repeated measures design D.C.Montgomery in his "Design and Analysis of Experiments" book provides the mathematical / statistical (linear) model (with changes): $y_{ij} = \mu + \beta_j + \tau_i + \epsilon_{ij}$, where $\beta$ is a parameter associated with the $j$th subject, $\tau$ is the effect of the $i$th treatment, and $\epsilon_{ij}$ is the independent error.
In Weixing Song's document (page 2) it is stated that to check the model's assumptions we should operate with residuals calculated as (A): $$\hat\epsilon_{ij} = Y_{ij} - \bar Y_{i.} - \bar Y_{.j} + \bar Y.$$

The formula (B) on Wikipedia is $$\hat\epsilon_i = Y_i - \bar Y.$$

My question is:
what formula is used to correctly calculate residuals in the model describing a single-factor repeated measures design to check its assumptions (multivariate normality, homoscedasticity, sphericity, linearity, additivity)?

Thank you.

P.S.
E.Vonesh and V.M.Chinchilli in their "Linear and Nonlinear Models for the Analysis of Repeated Measurements" monograph state that the single-sample RM design may be written as $y_{i} = \mu + \epsilon_{i}$.

Mod Removes Wiki by chl
deleted 8 characters in body
Source Link
abc
  • 1.8k
  • 3
  • 19
  • 33

For the repeated measures design D.C.Montgomery in his "Design and Analysis of Experiments" classic book provides the mathematical / statistical (linear) model: $y_{ij} = \mu + \tau_i+ \beta_j + \epsilon_{ij}$, where $\tau$ is the effect of the $i$th treatment, $\beta$ is a parameter associated with the $j$th subject, and $\epsilon_{ij}$ is the independent error.
In a (document, p. 2) it is stated that to check the model's assumptions we should operate with residuals calculated as (A): $$\hat\epsilon_{ij} = Y_{ij} - \bar Y_{i.} - \bar Y_{.j} + \bar Y.$$

The formula (B) on Wikipedia is $$\hat\epsilon_i = Y_i - \bar Y.$$

My question is:
what formula is used to correctly calculate residuals in the model describing a single-factor repeated measures design to check its assumptions (multivariate normality, homoscedasticity, sphericity, linearity, additivity)?

Thank you.


 

EDITp.S.
E.Vonesh and V.M.Chinchilli in their "Linear and Nonlinear Models for the Analysis of Repeated Measurements" monograph state that the single-sample RM design may be written as $y_{i} = \mu + \epsilon_{i}$.

For the repeated measures design D.C.Montgomery in his "Design and Analysis of Experiments" classic book provides the mathematical / statistical (linear) model: $y_{ij} = \mu + \tau_i+ \beta_j + \epsilon_{ij}$, where $\tau$ is the effect of the $i$th treatment, $\beta$ is a parameter associated with the $j$th subject, and $\epsilon_{ij}$ is the independent error.
In a (document, p. 2) it is stated that to check the model's assumptions we should operate with residuals calculated as (A): $$\hat\epsilon_{ij} = Y_{ij} - \bar Y_{i.} - \bar Y_{.j} + \bar Y.$$

The formula (B) on Wikipedia is $$\hat\epsilon_i = Y_i - \bar Y.$$

My question is:
what formula is used to correctly calculate residuals in the model describing a single-factor repeated measures design to check its assumptions (multivariate normality, homoscedasticity, sphericity, linearity, additivity)?

Thank you.


 

EDIT
E.Vonesh and V.M.Chinchilli in their "Linear and Nonlinear Models for the Analysis of Repeated Measurements" monograph state that the single-sample RM design may be written as $y_{i} = \mu + \epsilon_{i}$.

For the repeated measures design D.C.Montgomery in his "Design and Analysis of Experiments" book provides the mathematical / statistical (linear) model: $y_{ij} = \mu + \tau_i+ \beta_j + \epsilon_{ij}$, where $\tau$ is the effect of the $i$th treatment, $\beta$ is a parameter associated with the $j$th subject, and $\epsilon_{ij}$ is the independent error.
In a (document, p. 2) it is stated that to check the model's assumptions we should operate with residuals calculated as (A): $$\hat\epsilon_{ij} = Y_{ij} - \bar Y_{i.} - \bar Y_{.j} + \bar Y.$$

The formula (B) on Wikipedia is $$\hat\epsilon_i = Y_i - \bar Y.$$

My question is:
what formula is used to correctly calculate residuals in the model describing a single-factor repeated measures design to check its assumptions (multivariate normality, homoscedasticity, sphericity, linearity, additivity)?

Thank you.

p.S.
E.Vonesh and V.M.Chinchilli in their "Linear and Nonlinear Models for the Analysis of Repeated Measurements" monograph state that the single-sample RM design may be written as $y_{i} = \mu + \epsilon_{i}$.

edited body
Source Link
abc
  • 1.8k
  • 3
  • 19
  • 33
Loading
added 446 characters in body
Source Link
abc
  • 1.8k
  • 3
  • 19
  • 33
Loading
added 233 characters in body
Source Link
abc
  • 1.8k
  • 3
  • 19
  • 33
Loading
added 233 characters in body
Source Link
abc
  • 1.8k
  • 3
  • 19
  • 33
Loading
added 140 characters in body
Source Link
abc
  • 1.8k
  • 3
  • 19
  • 33
Loading
deleted 2 characters in body
Source Link
abc
  • 1.8k
  • 3
  • 19
  • 33
Loading
deleted 2 characters in body
Source Link
abc
  • 1.8k
  • 3
  • 19
  • 33
Loading
deleted 2 characters in body
Source Link
abc
  • 1.8k
  • 3
  • 19
  • 33
Loading
deleted 2 characters in body
Source Link
abc
  • 1.8k
  • 3
  • 19
  • 33
Loading
added 67 characters in body
Source Link
abc
  • 1.8k
  • 3
  • 19
  • 33
Loading
Source Link
abc
  • 1.8k
  • 3
  • 19
  • 33
Loading