R/example1.R
In myaseen208/agriTutorial: Tutorial Analysis of Some Agricultural Experiments
#' @title Example 1: Split-plot design with one qualitative and one quantitative level factor
#' @name example1
#' @aliases example1
#' @description Gomez & Gomez (1984, p. 143) report a rice experiment with three
#' management practices (minimum, optimum, intensive), five different amounts of
#' nitrogen (N) fertilizer (0, 50, 80, 110, 140 kg/ha), and three varieties (V1, V2, V3).
#' The experiment involved variety and management as qualitative treatment factors and
#' nitrogen fertilizer as a quantitative treatment factor. Overall,
#' there were 45 treatments with three replicates in complete replicate blocks.
#' The fertilizer treatments were applied to main plots, the management practices to
#' split-plots and the varieties to split-split-plots.
#'
#' @details
#' Section 1
#' Section 1 examines treatment effects by fitting qualitative factorial models and
#' the first analysis calculates a full analysis of variance (Table 1) for
#' main plots (nitrogen), split-plots (management) and split-split-plots (variety).
#' Each type of experimental unit (or "stratum") requires a separate error term in
#' the fitted analysis.
#'
#' The second analysis (Table 2) uses a REML mixed model analysis to find treatment means
#' and SE's for each marginal treatment classification averaged over all the
#' other treatment factors, together with estimates of pairwise contrasts of
#' treatment means and the SE's of the pairwise treatment comparisons.
#' This analysis fits the full set of nitrogen-by-variety interaction effects
#' assuming additive management effects and the fit of the model is tested by
#' a graphical plot of the model residuals. Residual plots provide an important
#' check on model assumptions but many more options for model testing are
#' available and further methods for diagnostic testing are examined in the
#' subsequent examples.
#'
#' The third analysis (Table 3) shows a mixed model analysis of the full factorial model
#' fitted by REML using the lmer function of the lme4 package. Generally with
#' mixed models, determination of the denominator degrees of freedom for
#' Wald-type F- and t-statistics becomes an issue, and here we use the
#' method proposed by Kenward & Roger (1997).
#'
#' Section 2
#' Section 2 examines treatment effects by fitting polynomial models and
#' the first step calculates a full set of four raw polynomials for the
#' 5-levels of N using the poly() function. The N rates are re-scaled by
#' division by 100 to improve numerical stability.
#'
#' The second step fits a mixed model polynomial analysis of nitrogen effects
#' assuming additive management effects (Table 7). In this analysis,
#' most of the nitrogen treatment effect can be explained by linear and
#' quadratic trend effects. but it is important to note that there is a
#' non-negligible Variety x Cubic N interaction effect. This suggests
#' that not all the varieties responded in a similar way to the N treatments
#' and that some further analysis of the data may be required
#' (see also the N plots of individual varieties and replicates in Fig 1).
#'
#' The third step fits the required model for the actual fitted model coefficients
#' (Table 8). When estimating model effects, only effects that are significant for
#' the fitted model or that are marginal to those effects (functional marginality)
#' should be included in the model therefore only linear and quadratic nitrogen effects
#' are included in this model. The fitted model for the nitrogen effects fits the actual
#' actual nitrogen levels used in the experiment therefore this model provides the
#' required coefficients for the actual applied nitrogen levels.
#'
#'
#' Section 3
#'
#' Section 3 provides checks on some of the assumptions underlying
#' the blocks-by-treatments model.
#'
#' The first analysis in this section shows a complete partition of
#' the blocks-by-treatments interaction effects into factorial mean
#' square terms where all the terms that contain a replicate:variety
#' interaction effect are estimates of the split-split-plot error
#' variance. If the blocks-by-treatments assumptions are valid,
#' all the estimates of the split-split-plot error variance are
#' expected to have the same error mean square. However,
#' the Replicate:variety effect has a mean square of 1.54 on 4
#' degrees of freedom whereas the Replicate:management:variety:nitrogen
#' effect has a mean square of 0.26 on 32 degrees of freedom.
#' The ratio of these mean squares is 5.92 with an F-probability of
#' 0.00110 on 4 and 32 degrees of freedom, which means that the
#' Replicate:variety interaction effect is significantly inflated
#' relative to the Replicate:management:variety:nitrogen effect.
#' This shows that the assumptions underlying the blocks-by-treatments
#' analysis of the model are invalid with a high level of probability.
#'
#' The 4 degrees of freedom in the Replicate:variety interaction
#' effect are the differences between the three varieties differenced
#' between the three replicate blocks. Fig S1 shows graphical plots
#' of variety effects in each replicate block averaged over management
#' effects, and there is clear evidence that the effects of Variety 1
#' in blocks 1 and 2 were different from the effects of Variety 1 in
#' block 3.
#'
#' The second analysis in Section 3 shows a complete partition of the
#' blocks-by-treatments interaction effects into factorial mean square
#' terms ignoring Variety 1. This analysis shows a reasonably good fit
#' to the assumed additive block which supports the hypothesis that
#' the non-additivity of the block-and-treatment effects in the full
#' unrestricted analysis is mainly due to Variety 1.
#'
#' The final analysis in Section 3 shows an analysis of variance of
#' the treatment effects ignoring Variety 1. In this analysis,
#' the management:variety interaction effect becomes significant at
#' the 0.00992 probability level compared with a non-significant
#' management:variety interaction effect in the analysis of the
#' full data set.
#'
#' Such anomalies are not uncommon in the analysis of real data sets
#' and it is the task of the statistician to identify anomalies as
#' and when they occur. Factorial designs can be very powerful for
#' practical research but, as demonstrated with this data set,
#' the analysis of such designs is complex and anomalies can be
#' easily missed. Unless an anomaly is due to an easily identified
#' cause such as an incorrectly recorded data point, it is likely
#' that the anomaly will need to be investigated by further
#' discussion with the research workers. It is a mistake to suppose
#' that data from a designed experiment can be analysed statistically
#' in isolation from the research workers who conducted the experiment.
#'
#' @author
#' \enumerate{
#' \item Rodney N. Edmondson (\email{rodney.edmondson@@gmail.com})
#' \item Hans-Peter Piepho (\email{piepho@@uni-hohenheim.de})
#' \item Muhammad Yaseen (\email{myaseen208@@gmail.com})
#' }
#'
#'
#'
#' @references
#' \enumerate{
#' \item Gomez, K. A., & Gomez, A. A. (1984). \emph{Statistical Procedures for Agricultural Research}. John Wiley & Sons.
#' \item Kenward, M. G., & Roger, J. H. (1997). Small sample inference for fixed effects from restricted maximum likelihood. \emph{Biometrics}, \strong{53}, 983–997.
#' \item Piepho, H., & Edmondson, R. (2018). A tutorial on the Statistical Analysis of Factorial Experiments with Qualitative and Quantitative treatment factor levels.
#' \emph{Journal of Agronomy and Crop Science.} (\url{https://onlinelibrary.wiley.com/doi/full/10.1111/jac.12267}).
#' }
#'
#' @importFrom broom tidy glance augment
#' @importFrom broom.mixed tidy glance augment
#' @importFrom dplyr filter group_by ungroup select summarise collapse
#' @importFrom emmeans emmeans contrast
#' @importFrom lmerTest lmer
#' @importFrom tidyr spread
#' @import ggfortify ggplot2 magrittr
#'
#'
#' @examples
#' library(broom)
#' library(broom.mixed)
#' library(dplyr)
#' library(emmeans)
#' library(ggfortify)
#' library(ggplot2)
#' library(lmerTest)
#' library(magrittr)
#' library(tidyr)
#'
#' options(contrasts = c('contr.treatment', 'contr.poly'))
#'
#' ##----fm1.1----
#' fm1.1 <- aov(yield ~ Replicate + nitrogen * management * variety +
#' Error(Replicate/nitrogen/management), rice)
#'
#' fm1.1.Summary <- broom::tidy(fm1.1)
#' fm1.1.Summary
#'
#' ##----fm1.2----
#' fm1.2 <- lmer(yield ~ Replicate + nitrogen * management * variety +
#' (1|Replicate:Main) + (1|Replicate:Main:Sub), data = rice)
#' fm1.2.ANOVA <- anova(fm1.2, ddf = "Kenward-Roger", type = 1)
#' fm1.2.ANOVA
#'
#'
#'
#' ##----fm1.3----
#' fm1.3 <- lmer(yield ~ Replicate + nitrogen + management + variety + nitrogen:variety +
#' (1|Replicate:Main) + (1|Replicate:Main:Sub), data = rice)
#' fm1.3.ANOVA <- anova(fm1.3, ddf = "Kenward-Roger", type = 1)
#'
#' emmeans::emmeans(fm1.3, ~ nitrogen)
#' emmeans::emmeans(fm1.3, ~ variety)
#' emmeans::emmeans(fm1.3, ~ nitrogen * variety)
#' emmeans::contrast(
#' emmeans::emmeans(fm1.3, ~ nitrogen|variety)
#' , alpha = 0.05
#' , method = "pairwise"
#' )
#'
#' emmeans::contrast(
#' emmeans::emmeans(fm1.3, ~ variety|nitrogen)
#' , alpha = 0.05
#' , method = "pairwise"
#' )
#'
#' ##----fm1.3.Plot----
#' fm1.3.Augment <- broom.mixed::augment(fm1.3)
#'
#' ggplot(data = fm1.3.Augment, mapping = aes(x = .fitted, y = .resid)) +
#' geom_point() +
#' geom_hline(yintercept = 0) +
#' labs(
#' x = "Fitted"
#' , y = "Residuals"
#' , title = "Full analysis with full nitrogen effects") +
#' theme_bw() +
#' theme(plot.title = element_text(hjust = 0.5))
#'
#'
#' ##----fm1.4----
#' fm1.4 <- lmer(yield ~ Replicate + nitrogen * management * variety + (1|Replicate:Main) +
#' (1|Replicate:Main:Sub), data = rice)
#' fm1.4.ANOVA <- anova(fm1.4, ddf = "Kenward-Roger", type = 1)
#'
#' fm1.4.ANOVA
#'
#' ##----fm1.5----
#' fm1.5 <- lmer(yield ~ Replicate + management + variety * (nrate + I(nrate^2) +
#' I(nrate^3) + I(nrate^4)) +
#' (1|Replicate:Main) + (1|Replicate:Main:Sub), data = rice)
#' fm1.5.ANOVA <- anova(fm1.5, ddf = "Kenward-Roger", type = 1)
#'
#' fm1.5.ANOVA
#'
#' ##----fm1.6----
#' fm1.6 <- lmer(yield ~ Replicate + management + variety * nrate + I(nrate^2) +
#' (1|Replicate:Main) + (1|Replicate:Main:Sub), data = rice)
#'
#' fm1.6.Coef <- summary(fm1.6, ddf = "Kenward-Roger")$coef
#' fm1.6.Coef
#'
#' ##----fm1.6.Coefs----
#' # fm1.6.Coef[ ,1, drop = FALSE]
#'
#' # Intercepts
#' fm1.6.Coef[1, 1] + sum(fm1.6.Coef[2:3, 1])/3 + sum(fm1.6.Coef[4:5, 1])/3
#' fm1.6.Coef[1, 1] + sum(fm1.6.Coef[2:3, 1])/3 + sum(fm1.6.Coef[4:5, 1])/3 +
#' fm1.6.Coef[6, 1]
#' fm1.6.Coef[1, 1] + sum(fm1.6.Coef[2:3, 1])/3 + sum(fm1.6.Coef[4:5, 1])/3 +
#' fm1.6.Coef[7, 1]
#'
#' # Linear Slopes
#' fm1.6.Coef[8, 1]
#' fm1.6.Coef[8, 1] + fm1.6.Coef[10, 1]
#' fm1.6.Coef[8, 1] + fm1.6.Coef[11, 1]
#'
#' # Quadratic Slopes
#' fm1.6.Coef[9, 1]
#'
#' ##----fm1.7----
#' fm1.7 <- aov(yield ~ Replicate*management * variety * nitrogen, rice)
#' fm1.7.Summary <- broom::tidy(fm1.7)
#'
#' fm1.7.Summary
#'
#' ##----fm1.7.Rice----
#' Rice1 <-
#' rice %>%
#' dplyr::group_by(Replicate, nitrogen, variety) %>%
#' dplyr::summarise(Yield = mean(yield, na.rm = TRUE))
#'
#' Rice1
#'
#' WideRice1 <-
#' Rice1 %>%
#' tidyr::spread(key = nitrogen, value = Yield) %>%
#' dplyr::ungroup() %>%
#' dplyr::select(-Replicate, -variety)
#'
#'
#' ##----fm1.7.Plot1----
#' ggplot(data = Rice1, mapping = aes(x = nitrogen, y = Yield, group = Replicate)) +
#' geom_line() +
#' facet_grid(variety ~ Replicate, labeller = label_both) +
#' labs(
#' x = "Nitrogen"
#' , y = "Yield"
#' , title = "Fig S1. Variety response to nitrogen for individual replicate blocks"
#' ) +
#' theme_bw() +
#' theme(plot.title = element_text(hjust = 0.5))
#'
#'
#'
#' ##----fm1.8----
#' riceV2V3 <-
#' rice %>%
#' dplyr::filter(variety != "V1") %>%
#' droplevels()
#'
#' fm1.8 <- aov(yield ~ Replicate*management * variety * nitrogen, riceV2V3)
#' fm1.8.ANOVA <- broom::tidy(fm1.8)
#'
#' fm1.8.ANOVA
#'
#' ##----fm1.9----
#' fm1.9 <- aov(yield ~ Replicate + management * variety * nitrogen +
#' Error(Replicate/Main/Sub), riceV2V3)
#' fm1.9.ANOVA <- broom::tidy(fm1.9)
#' fm1.9.ANOVA
#'
NULL
myaseen208/agriTutorial documentation built on Feb. 25, 2020, 12:01 a.m.
R Package Documentation
Browse R Packages
We want your feedback!
Note that we can't provide technical support on individual packages. You should contact the package authors for that.
#' @title Example 1: Split-plot design with one qualitative and one quantitative level factor
#' @name example1
#' @aliases example1
#' @description Gomez & Gomez (1984, p. 143) report a rice experiment with three
#' management practices (minimum, optimum, intensive), five different amounts of
#' nitrogen (N) fertilizer (0, 50, 80, 110, 140 kg/ha), and three varieties (V1, V2, V3).
#' The experiment involved variety and management as qualitative treatment factors and
#' nitrogen fertilizer as a quantitative treatment factor. Overall,
#' there were 45 treatments with three replicates in complete replicate blocks.
#' The fertilizer treatments were applied to main plots, the management practices to
#' split-plots and the varieties to split-split-plots.
#'
#' @details
#' Section 1
#' Section 1 examines treatment effects by fitting qualitative factorial models and
#' the first analysis calculates a full analysis of variance (Table 1) for
#' main plots (nitrogen), split-plots (management) and split-split-plots (variety).
#' Each type of experimental unit (or "stratum") requires a separate error term in
#' the fitted analysis.
#'
#' The second analysis (Table 2) uses a REML mixed model analysis to find treatment means
#' and SE's for each marginal treatment classification averaged over all the
#' other treatment factors, together with estimates of pairwise contrasts of
#' treatment means and the SE's of the pairwise treatment comparisons.
#' This analysis fits the full set of nitrogen-by-variety interaction effects
#' assuming additive management effects and the fit of the model is tested by
#' a graphical plot of the model residuals. Residual plots provide an important
#' check on model assumptions but many more options for model testing are
#' available and further methods for diagnostic testing are examined in the
#' subsequent examples.
#'
#' The third analysis (Table 3) shows a mixed model analysis of the full factorial model
#' fitted by REML using the lmer function of the lme4 package. Generally with
#' mixed models, determination of the denominator degrees of freedom for
#' Wald-type F- and t-statistics becomes an issue, and here we use the
#' method proposed by Kenward & Roger (1997).
#'
#' Section 2
#' Section 2 examines treatment effects by fitting polynomial models and
#' the first step calculates a full set of four raw polynomials for the
#' 5-levels of N using the poly() function. The N rates are re-scaled by
#' division by 100 to improve numerical stability.
#'
#' The second step fits a mixed model polynomial analysis of nitrogen effects
#' assuming additive management effects (Table 7). In this analysis,
#' most of the nitrogen treatment effect can be explained by linear and
#' quadratic trend effects. but it is important to note that there is a
#' non-negligible Variety x Cubic N interaction effect. This suggests
#' that not all the varieties responded in a similar way to the N treatments
#' and that some further analysis of the data may be required
#' (see also the N plots of individual varieties and replicates in Fig 1).
#'
#' The third step fits the required model for the actual fitted model coefficients
#' (Table 8). When estimating model effects, only effects that are significant for
#' the fitted model or that are marginal to those effects (functional marginality)
#' should be included in the model therefore only linear and quadratic nitrogen effects
#' are included in this model. The fitted model for the nitrogen effects fits the actual
#' actual nitrogen levels used in the experiment therefore this model provides the
#' required coefficients for the actual applied nitrogen levels.
#'
#'
#' Section 3
#'
#' Section 3 provides checks on some of the assumptions underlying
#' the blocks-by-treatments model.
#'
#' The first analysis in this section shows a complete partition of
#' the blocks-by-treatments interaction effects into factorial mean
#' square terms where all the terms that contain a replicate:variety
#' interaction effect are estimates of the split-split-plot error
#' variance. If the blocks-by-treatments assumptions are valid,
#' all the estimates of the split-split-plot error variance are
#' expected to have the same error mean square. However,
#' the Replicate:variety effect has a mean square of 1.54 on 4
#' degrees of freedom whereas the Replicate:management:variety:nitrogen
#' effect has a mean square of 0.26 on 32 degrees of freedom.
#' The ratio of these mean squares is 5.92 with an F-probability of
#' 0.00110 on 4 and 32 degrees of freedom, which means that the
#' Replicate:variety interaction effect is significantly inflated
#' relative to the Replicate:management:variety:nitrogen effect.
#' This shows that the assumptions underlying the blocks-by-treatments
#' analysis of the model are invalid with a high level of probability.
#'
#' The 4 degrees of freedom in the Replicate:variety interaction
#' effect are the differences between the three varieties differenced
#' between the three replicate blocks. Fig S1 shows graphical plots
#' of variety effects in each replicate block averaged over management
#' effects, and there is clear evidence that the effects of Variety 1
#' in blocks 1 and 2 were different from the effects of Variety 1 in
#' block 3.
#'
#' The second analysis in Section 3 shows a complete partition of the
#' blocks-by-treatments interaction effects into factorial mean square
#' terms ignoring Variety 1. This analysis shows a reasonably good fit
#' to the assumed additive block which supports the hypothesis that
#' the non-additivity of the block-and-treatment effects in the full
#' unrestricted analysis is mainly due to Variety 1.
#'
#' The final analysis in Section 3 shows an analysis of variance of
#' the treatment effects ignoring Variety 1. In this analysis,
#' the management:variety interaction effect becomes significant at
#' the 0.00992 probability level compared with a non-significant
#' management:variety interaction effect in the analysis of the
#' full data set.
#'
#' Such anomalies are not uncommon in the analysis of real data sets
#' and it is the task of the statistician to identify anomalies as
#' and when they occur. Factorial designs can be very powerful for
#' practical research but, as demonstrated with this data set,
#' the analysis of such designs is complex and anomalies can be
#' easily missed. Unless an anomaly is due to an easily identified
#' cause such as an incorrectly recorded data point, it is likely
#' that the anomaly will need to be investigated by further
#' discussion with the research workers. It is a mistake to suppose
#' that data from a designed experiment can be analysed statistically
#' in isolation from the research workers who conducted the experiment.
#'
#' @author
#' \enumerate{
#' \item Rodney N. Edmondson (\email{rodney.edmondson@@gmail.com})
#' \item Hans-Peter Piepho (\email{piepho@@uni-hohenheim.de})
#' \item Muhammad Yaseen (\email{myaseen208@@gmail.com})
#' }
#'
#'
#'
#' @references
#' \enumerate{
#' \item Gomez, K. A., & Gomez, A. A. (1984). \emph{Statistical Procedures for Agricultural Research}. John Wiley & Sons.
#' \item Kenward, M. G., & Roger, J. H. (1997). Small sample inference for fixed effects from restricted maximum likelihood. \emph{Biometrics}, \strong{53}, 983–997.
#' \item Piepho, H., & Edmondson, R. (2018). A tutorial on the Statistical Analysis of Factorial Experiments with Qualitative and Quantitative treatment factor levels.
#' \emph{Journal of Agronomy and Crop Science.} (\url{https://onlinelibrary.wiley.com/doi/full/10.1111/jac.12267}).
#' }
#'
#' @importFrom broom tidy glance augment
#' @importFrom broom.mixed tidy glance augment
#' @importFrom dplyr filter group_by ungroup select summarise collapse
#' @importFrom emmeans emmeans contrast
#' @importFrom lmerTest lmer
#' @importFrom tidyr spread
#' @import ggfortify ggplot2 magrittr
#'
#'
#' @examples
#' library(broom)
#' library(broom.mixed)
#' library(dplyr)
#' library(emmeans)
#' library(ggfortify)
#' library(ggplot2)
#' library(lmerTest)
#' library(magrittr)
#' library(tidyr)
#'
#' options(contrasts = c('contr.treatment', 'contr.poly'))
#'
#' ##----fm1.1----
#' fm1.1 <- aov(yield ~ Replicate + nitrogen * management * variety +
#' Error(Replicate/nitrogen/management), rice)
#'
#' fm1.1.Summary <- broom::tidy(fm1.1)
#' fm1.1.Summary
#'
#' ##----fm1.2----
#' fm1.2 <- lmer(yield ~ Replicate + nitrogen * management * variety +
#' (1|Replicate:Main) + (1|Replicate:Main:Sub), data = rice)
#' fm1.2.ANOVA <- anova(fm1.2, ddf = "Kenward-Roger", type = 1)
#' fm1.2.ANOVA
#'
#'
#'
#' ##----fm1.3----
#' fm1.3 <- lmer(yield ~ Replicate + nitrogen + management + variety + nitrogen:variety +
#' (1|Replicate:Main) + (1|Replicate:Main:Sub), data = rice)
#' fm1.3.ANOVA <- anova(fm1.3, ddf = "Kenward-Roger", type = 1)
#'
#' emmeans::emmeans(fm1.3, ~ nitrogen)
#' emmeans::emmeans(fm1.3, ~ variety)
#' emmeans::emmeans(fm1.3, ~ nitrogen * variety)
#' emmeans::contrast(
#' emmeans::emmeans(fm1.3, ~ nitrogen|variety)
#' , alpha = 0.05
#' , method = "pairwise"
#' )
#'
#' emmeans::contrast(
#' emmeans::emmeans(fm1.3, ~ variety|nitrogen)
#' , alpha = 0.05
#' , method = "pairwise"
#' )
#'
#' ##----fm1.3.Plot----
#' fm1.3.Augment <- broom.mixed::augment(fm1.3)
#'
#' ggplot(data = fm1.3.Augment, mapping = aes(x = .fitted, y = .resid)) +
#' geom_point() +
#' geom_hline(yintercept = 0) +
#' labs(
#' x = "Fitted"
#' , y = "Residuals"
#' , title = "Full analysis with full nitrogen effects") +
#' theme_bw() +
#' theme(plot.title = element_text(hjust = 0.5))
#'
#'
#' ##----fm1.4----
#' fm1.4 <- lmer(yield ~ Replicate + nitrogen * management * variety + (1|Replicate:Main) +
#' (1|Replicate:Main:Sub), data = rice)
#' fm1.4.ANOVA <- anova(fm1.4, ddf = "Kenward-Roger", type = 1)
#'
#' fm1.4.ANOVA
#'
#' ##----fm1.5----
#' fm1.5 <- lmer(yield ~ Replicate + management + variety * (nrate + I(nrate^2) +
#' I(nrate^3) + I(nrate^4)) +
#' (1|Replicate:Main) + (1|Replicate:Main:Sub), data = rice)
#' fm1.5.ANOVA <- anova(fm1.5, ddf = "Kenward-Roger", type = 1)
#'
#' fm1.5.ANOVA
#'
#' ##----fm1.6----
#' fm1.6 <- lmer(yield ~ Replicate + management + variety * nrate + I(nrate^2) +
#' (1|Replicate:Main) + (1|Replicate:Main:Sub), data = rice)
#'
#' fm1.6.Coef <- summary(fm1.6, ddf = "Kenward-Roger")$coef
#' fm1.6.Coef
#'
#' ##----fm1.6.Coefs----
#' # fm1.6.Coef[ ,1, drop = FALSE]
#'
#' # Intercepts
#' fm1.6.Coef[1, 1] + sum(fm1.6.Coef[2:3, 1])/3 + sum(fm1.6.Coef[4:5, 1])/3
#' fm1.6.Coef[1, 1] + sum(fm1.6.Coef[2:3, 1])/3 + sum(fm1.6.Coef[4:5, 1])/3 +
#' fm1.6.Coef[6, 1]
#' fm1.6.Coef[1, 1] + sum(fm1.6.Coef[2:3, 1])/3 + sum(fm1.6.Coef[4:5, 1])/3 +
#' fm1.6.Coef[7, 1]
#'
#' # Linear Slopes
#' fm1.6.Coef[8, 1]
#' fm1.6.Coef[8, 1] + fm1.6.Coef[10, 1]
#' fm1.6.Coef[8, 1] + fm1.6.Coef[11, 1]
#'
#' # Quadratic Slopes
#' fm1.6.Coef[9, 1]
#'
#' ##----fm1.7----
#' fm1.7 <- aov(yield ~ Replicate*management * variety * nitrogen, rice)
#' fm1.7.Summary <- broom::tidy(fm1.7)
#'
#' fm1.7.Summary
#'
#' ##----fm1.7.Rice----
#' Rice1 <-
#' rice %>%
#' dplyr::group_by(Replicate, nitrogen, variety) %>%
#' dplyr::summarise(Yield = mean(yield, na.rm = TRUE))
#'
#' Rice1
#'
#' WideRice1 <-
#' Rice1 %>%
#' tidyr::spread(key = nitrogen, value = Yield) %>%
#' dplyr::ungroup() %>%
#' dplyr::select(-Replicate, -variety)
#'
#'
#' ##----fm1.7.Plot1----
#' ggplot(data = Rice1, mapping = aes(x = nitrogen, y = Yield, group = Replicate)) +
#' geom_line() +
#' facet_grid(variety ~ Replicate, labeller = label_both) +
#' labs(
#' x = "Nitrogen"
#' , y = "Yield"
#' , title = "Fig S1. Variety response to nitrogen for individual replicate blocks"
#' ) +
#' theme_bw() +
#' theme(plot.title = element_text(hjust = 0.5))
#'
#'
#'
#' ##----fm1.8----
#' riceV2V3 <-
#' rice %>%
#' dplyr::filter(variety != "V1") %>%
#' droplevels()
#'
#' fm1.8 <- aov(yield ~ Replicate*management * variety * nitrogen, riceV2V3)
#' fm1.8.ANOVA <- broom::tidy(fm1.8)
#'
#' fm1.8.ANOVA
#'
#' ##----fm1.9----
#' fm1.9 <- aov(yield ~ Replicate + management * variety * nitrogen +
#' Error(Replicate/Main/Sub), riceV2V3)
#' fm1.9.ANOVA <- broom::tidy(fm1.9)
#' fm1.9.ANOVA
#'
NULL
R Package Documentation
Browse R Packages
We want your feedback!
Note that we can't provide technical support on individual packages. You should contact the package authors for that.
Embedding an R snippet on your website
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.