RJ-2024-011 remove blue text

Author: mitchelloharawild

_articles/RJ-2024-011/RJ-2024-011.Rmd

@@ -155,7 +155,7 @@ of syllables making up the songs as well as the lengths of
 inter-syllable intervals (ISIs). The data set `foxp2` included in the
 **BMRMM** package is taken from the simulation study of
 [@wu2021bayesian]. It is much shorter than the real FoxP2 data set but
-closely mimics its other aspects and is used]{style="color: blue"} in
+closely mimics its other aspects and is used] in
 this paper to demonstrate how to obtain detailed inferences for both
 syllable transitions and ISI dynamics for a comprehensive analysis of
 the vocal repertoire in mice with and without the FoxP2 mutation.
@@ -215,7 +215,7 @@ Bayesian M(R)MMs.
 Documentation for the functions of the **BMRMM** package is then
 provided. Next, we demonstrate the usage of our package in analyzing two
 different data sets. The final section contains some concluding remarks.
-]{style="color: blue"}
+]
 
 ## The Bayesian Markov (renewal) mixed models {#sec:models}
 
@@ -276,7 +276,7 @@ $\boldsymbol\lambda_{trans,x_1=1,x_2,\dots,x_p}(\cdot\mid y_{t-1})$ and
 $\boldsymbol\lambda_{trans,x_1=2,x_2,\dots,x_p}(\cdot\mid y_{t-1})$ would be
 equal if levels 1 and 2 of covariate 1 have similar influences on
 transition dynamics for fixed levels for covariates
-$2, \dots, p$.]{style="color: blue"} A clustering mechanism for
+$2, \dots, p$.] A clustering mechanism for
 covariate levels allows the fixed component
 $\boldsymbol\lambda_{trans,x_1,\dots,x_p}(\cdot\mid y_{t-1})$ to be the same
 for all levels with a similar influence. In particular, for covariate
@@ -289,7 +289,7 @@ indicate the cluster index for the $\ell^{th}$ label of covariate $j$.
 [Two levels of the covariate $j$,
 $\ell_1, \ell_2 \in {\cal X}_j = \{1,\dots,d_j\}$, are clustered
 together if and only if
-$z_{trans,j,\ell_1} = z_{trans,j,\ell_2}$.]{style="color: blue"} For the
+$z_{trans,j,\ell_1} = z_{trans,j,\ell_2}$.] For the
 fixed effects, we then replace the covariate levels $x_1,\dots,x_p$'s
 with cluster indices $h_1,\dots,h_p$'s and present the fixed effect as
 $\boldsymbol\lambda_{trans,h_{1},\dots,h_{p}}(\cdot\mid y_{t-1})$.
@@ -410,7 +410,7 @@ Inference is based on samples drawn from the posterior using a
 [Metropolis-Hastings-within-Gibbs MCMC algorithm. Most full conditionals
 are available in closed form and can be directly sampled from. A
 Metropolis-Hastings step is however used for updating the discrete
-valued cluster configurations.]{style="color: blue"} There is, however,
+valued cluster configurations.] There is, however,
 no conjugate prior for gamma distributions with unknown shape parameters
 [@damsleth1975conjugate]. Recently, @miller2019fast designed a procedure
 that efficiently approximates the posterior full conditionals of gamma
@@ -428,7 +428,7 @@ out detailed analyses of the state transitions and their duration times
 package includes a number of supplementary functions that use the
 results of the main function to produce numerical summaries,
 visualizations, and diagnostics. Table \@ref(tab:fn) provides a brief
-description of all functions. ]{style="color: blue"}
+description of all functions. ]
 
 ::: {#tab:fn}
 ```{r fn, echo = FALSE, results = 'asis'}
@@ -453,7 +453,7 @@ BMRMM(data, num.cov, cov.labels = NULL, state.labels = NULL,
 ```
 
 [The parameter `data` specifies the target data set and needs to follow
-a certain structure. ]{style="color: blue"} The first column should list
+a certain structure. ] The first column should list
 the individual IDs $i_{s}$, followed by $p$ columns for the values of
 the $p$ associated covariates $x_{s,j}$, then two columns for the values
 of the previous state $y_{s,t-1}$, the current state $y_{s,t}$, and
@@ -462,7 +462,7 @@ one to five categorical covariates that take on values ${1,2,\dots}$.
 The duration times column is optional if the user would like to use BMMM
 instead of BMRMM to analyze just the state transitions. This is shown in
 Table [2](#tab:data-cols). The users can look at the included
-[simulated data set]{style="color: blue"} `foxp2` as an example.
+[simulated data set] `foxp2` as an example.
 
 ::: {#tab:data-cols}
   ---------------------------------------------------------------------------------------------------
@@ -479,33 +479,33 @@ Table [2](#tab:data-cols). The users can look at the included
 names of covariate levels in the covariate order that is presented in
 `data` while the parameter `state.labels` is a vector providing the
 names of the transition states. The default labels are Arabic numerals.
-]{style="color: blue"} The [`random.effect`]{style="color: blue"}
+] The [`random.effect`]
 parameter gives users the option to exclude the random individual
-effects. If [`random.effect`]{style="color: blue"} is set to `FALSE`,
+effects. If [`random.effect`] is set to `FALSE`,
 the transition probabilities (and the mixture probabilities for duration
 times, if applicable) will only consider the influence of the covariate
-levels. Similarly, the [`fixed.effect`]{style="color: blue"} parameter
+levels. Similarly, the [`fixed.effect`] parameter
 allows users to exclude the fixed population effects. [The default
 values for `random.effect` and `fixed.effect` are both
-`TRUE`.]{style="color: blue"} The covariate indices for the two analyses
+`TRUE`.] The covariate indices for the two analyses
 can be specified by setting `trans.cov.index` and `duration.cov.index`.
 [We note that indices specified by `trans.cov.index` and
 `duration.cov.index` refer to the index of the covariate when the first
 covariate is given index 1, thus different from its index in
-`data`.]{style="color: blue"}
+`data`.]
 
 [Users can define `duration.distr` in the following three
-ways.]{style="color: blue"}
+ways.]
 
 1.  [If users set `duration.distr` to be `NULL`, which is the default
     setting, then the duration times will be ignored and not modeled at
-    all. ]{style="color: blue"} The BMMM described will be implemented
+    all. ] The BMMM described will be implemented
     to analyze the existing state transitions alone.
 
 2.  [If `duration.distr` is set as `list(‘mixDirichlet’, unit)`, the
     duration times will be used to construct a new state `‘dur.state’`,
     which will be analyzed along with the original set of states.
-    ]{style="color: blue"} The additional argument `unit` must be
+    ] The additional argument `unit` must be
     defined and acts both as a threshold and as a block size for
     duration times. For example, if the `unit` is set to $5$, then for
     each duration value greater than $5$ units, each block of $5$ unit
@@ -515,7 +515,7 @@ ways.]{style="color: blue"}
     seconds, then the updated Markov sequence will contain three
     consecutive `‘dur.state’` states, i.e.,
     `(‘a’, ‘dur.state’, ‘dur.state’, ‘dur.state’, ‘b’)`.
-    ]{style="color: blue"} Since we adopt the floor operation, a
+    ] Since we adopt the floor operation, a
     duration time of say $17.68$ seconds will also be replaced by three
     consecutive instances of `’dur.state’` states in this example. The
     BMMM model will then be implemented to analyze the resulting
@@ -528,19 +528,19 @@ ways.]{style="color: blue"}
 3.  [If `duration.distr` is set to be `list(‘mixgamma’, shape, rate)`,
     the duration times are modeled as a continuous random variable using
     a flexible mixture of gamma kernels, as described for a BMRMM
-    model.]{style="color: blue"} In this case, users can specify the
+    model.] In this case, users can specify the
     prior shape and rate parameters with the `shape` and `rate`
     arguments within the definition of `duration.distr`. We note that
     `shape` and `rate` must be numeric vectors of the same length.
 
 By default, we consider the previous state $y_{s,t-1}$ as a covariate
 when we model the duration times as continuous variables, i.e.,
-[`duration.incl.prev.state`]{style="color: blue"} is set to `TRUE`.
+[`duration.incl.prev.state`] is set to `TRUE`.
 Users can set this parameter to `FALSE` if they wish to exclude the
 previous state when analyzing the duration times. [The remaining
 parameters `simsize` and `burnin` denote the total number of MCMC
 iterations and the number of burn-ins, respectively.
-]{style="color: blue"}
+]
 
 ::: {#tab:bmrmm}
   ----------------------------------------------------------------------------------------------------------------------------------------------------------------
@@ -550,21 +550,21 @@ iterations and the number of burn-ins, respectively.
 
   `num.cov`                                           an integer giving the number of observed covariates in `data`                
 
-  [`cov.labels`]{style="color: blue"}                 a list of vectors giving names of all covariate levels                       [`NULL`]{style="color: blue"}
+  [`cov.labels`]                 a list of vectors giving names of all covariate levels                       [`NULL`]
 
-  [`state.labels`]{style="color: blue"}               a vector giving names of the states                                          [`NULL`]{style="color: blue"}
+  [`state.labels`]               a vector giving names of the states                                          [`NULL`]
 
-  [`random.effect`]{style="color: blue"}              `TRUE` if random individual effects are included                             [`TRUE`]{style="color: blue"}
+  [`random.effect`]              `TRUE` if random individual effects are included                             [`TRUE`]
 
-  [`fixed.effect`]{style="color: blue"}               `TRUE` if fixed population effects are included                              [`TRUE`]{style="color: blue"}
+  [`fixed.effect`]               `TRUE` if fixed population effects are included                              [`TRUE`]
 
   `trans.cov.index`                                   selects the covariates to analyze for transition probabilities               `1:num.cov`
 
   `duration.cov.index`                                selects the covariates to analyze for duration times                         `1:num.cov`
 
   `duration.distr`                                    specifies the distribution for duration times                                `NULL`
 
-  [`duration.incl.prev.state`]{style="color: blue"}   `TRUE` if $y_{t-1}$ acts as a covariate for the analysis of duration times   [`TRUE`]{style="color: blue"}
+  [`duration.incl.prev.state`]   `TRUE` if $y_{t-1}$ acts as a covariate for the analysis of duration times   [`TRUE`]
 
   `simsize`                                           number of MCMC iterations                                                    10000
 
@@ -577,7 +577,7 @@ iterations and the number of burn-ins, respectively.
 The `BMRMM` function returns [an object of class `BMRMM`, which either
 contains only `results.trans` or both of `results.trans` and
 `results.duration` if duration times follow a mixture gamma
-distribution.]{style="color: blue"} For the state transitions, the
+distribution.] For the state transitions, the
 posterior mean transition probability matrices for each combination of
 the covariate levels and each individual are given by
 `results.trans$tp.exgns.post.mean` and
@@ -593,10 +593,10 @@ transition probabilities, `results.duration$clusters` gives the cluster
 configurations of the covariates. Other elements of `results.trans` and
 `results.duration` can be found in the detailed R function description.
 
-### [Summarizing BMRMM results]{style="color: blue"}
+### [Summarizing BMRMM results]
 
 [The **BMRMM** package provides an S3 method for summarizing results of
-a `BMRMM` object as follows. ]{style="color: blue"}
+a `BMRMM` object as follows. ]
 
 ``` r
 summary.BMRMM(object, delta = 0.02, digits = 2, ...)
@@ -607,14 +607,14 @@ associated with local tests for transition probabilities, which we will
 explain further. The `digit` parameter is an integer used for number
 formatting, as in the general `summary` function. The `summary.BMRMM`
 function returns an object of class `BMRMMsummary` with the following
-fields. ]{style="color: blue"}
+fields. ]
 
 -   `trans.global` and `dur.global`
 
     [These two fields give the global test results from the inference of
     transition probabilities and duration times. Global tests show the
     significance of the covariates in affecting the state transitions
-    and duration times. ]{style="color: blue"} Specifically, for each
+    and duration times. ] Specifically, for each
     covariate, the empirical distribution of the size of the clusters in
     the stored MCMC iterations is calculated. The null hypothesis that a
     covariate is not important is equivalent to the event that all its
@@ -633,15 +633,15 @@ fields. ]{style="color: blue"}
     transition probabilities. Local tests analyze the differences
     between the transition probabilities associated with two different
     levels of a covariate $j$, fixing the levels of the other
-    covariates.]{style="color: blue"} For every pair of levels of
+    covariates.] For every pair of levels of
     covariate $j$, `trans.local.mean.diff` gives the absolute
     differences in transition probabilities for each transition type in
     the MCMC iterations. The local null hypothesis we test for each
     transition type is that this difference is at least the
     pre-specified value `delta`. [Meanwhile, `trans.local.null.test`
     gives the probability of the null hypothesis that the difference
     between two covariate levels is not significant under each
-    transition type. ]{style="color: blue"}
+    transition type. ]
 
 -   `dur.mix.params` and `dur.mix.probs`
 
@@ -651,7 +651,7 @@ fields. ]{style="color: blue"}
     probabilities by calling the field `dur.mix.probs`, which can be
     further used to estimate the length of the duration times.
 
-### [Visualizing results with BMRMM plotting functions]{style="color: blue"}
+### [Visualizing results with BMRMM plotting functions]
 
 [The main plotting function of the package, `plot.BMRMMsummary`, is an
 S3 method for class `BMRMMsummary`. It gives the barplots for global
@@ -661,7 +661,7 @@ mixture parameters and probabilities for duration times. The parameters
 of `plot.BMRMMsummary` include `x`, which must be an object of class
 `BMRMMsummary` and `type`, which is a single string representing the
 field of `x` that needs to be plotted. The function also takes general
-plotting arguments such as `xlab`, `ylab`, etc. ]{style="color: blue"}
+plotting arguments such as `xlab`, `ylab`, etc. ]
 
 ``` r
 plot.BMRMMsummary(x, type, xlab = NULL, ylab = NULL, main = NULL, col = NULL, ...)
@@ -681,7 +681,7 @@ component `comp` will be presented alongside the mixture gamma
 distribution with the shape and rate parameters from the last MCMC
 iteration. Users can refer to the documentation of the general `hist`
 function to see the interpretation for the rest of the parameters.
-]{style="color: blue"}
+]
 
 ``` r
 hist.BMRMM(x, comp = NULL, xlim = NULL, breaks = NULL, main = NULL, 
@@ -696,13 +696,13 @@ state transitions they are interested in by defining `cov.combs` and
 `transitions`, respectively. For duration times, users can define
 `components`, a numeric vector, to obtain the diagnostic plots for shape
 and rate parameters of the specific component
-kernels.]{style="color: blue"}
+kernels.]
 
 ``` r
 diag.BMRMM(object, cov.combs = NULL, transitions = NULL, components = NULL) 
 ```
 
-### [Model selection scores for continuous duration times]{style="color: blue"}
+### [Model selection scores for continuous duration times]
 
 When the duration times are modeled using mixtures of gamma
 distributions, model selection can be performed on the number of mixture
@@ -713,7 +713,7 @@ model.selection.scores(object)
 ```
 
 [The function takes an `object` as its input, which must be an object of
-class `BMRMM`. It returns a list consisting of]{style="color: blue"} the
+class `BMRMM`. It returns a list consisting of] the
 log pseudo marginal likelihood (LPML) [@geisser1979predictive] and the
 widely applicable information criterion (WAIC) [@watanabe2010asymptotic]
 scores of the model. Larger values of LPML and smaller values of WAIC
@@ -738,7 +738,7 @@ gene on human vocal communication abilities and related deficiencies.
 simulated a data set that closely mimics the real one. For demonstrating
 the **BMRMM** package, we included in it a shortened version of this
 synthetic data set which we refer to as the `foxp2` data set.
-]{style="color: blue"} The `foxp2` synthetic data set has $17391$ rows
+] The `foxp2` synthetic data set has $17391$ rows
 and $6$ columns, which are Id, Genotype, Context, Prev_State, Cur_State,
 and Transformed_ISI. The original FoxP2 data set records ISIs in
 seconds. In the simulated data set `foxp2`, following @wu2021bayesian,
@@ -818,7 +818,7 @@ test results for identifying the significant covariates can be found by
 calling the fields `trans.global` and `dur.global`. The function
 `plot.BMRMMsummary` is called to visualize the global tests using
 barplots, as presented in Figure \@ref(fig:figglobal).
-]{style="color: blue"} We recall that a covariate is significant when
+] We recall that a covariate is significant when
 its levels formed more than one cluster with very high posterior
 probability (the bar heights). Figure \@ref(fig:figglobal) and the
 printed results suggest that every covariate is significant for the ISIs
@@ -848,7 +848,7 @@ knitr::include_graphics(c("figs/global_trans_foxp2.png", "figs/global_isi_foxp2.
 
 [The plotting function can be called to visualize the posterior
 transition probabilities under different combinations of the covariate
-levels. ]{style="color: blue"} We show in Figure \@ref(fig:figpost-mean)
+levels. ] We show in Figure \@ref(fig:figpost-mean)
 the heatmaps for the posterior mean and standard deviation of the
 transition probabilities for each transition type for the following
 combinations of covariates: $(F,A)$ and $(W,L)$.
@@ -877,7 +877,7 @@ results if we set the `type` to be `‘trans.local.mean.diff’` or
 `‘trans.local.null.test’`. Here, we show the results of local tests for
 the covariate 1 (i.e., genotype) with `delta` equaling the default value
 of 0.02, and present the plots in
-Figure \@ref(fig:figlocal).]{style="color: blue"} From the figure, we
+Figure \@ref(fig:figlocal).] From the figure, we
 see that the posterior probabilities of the null hypotheses are
 generally large for most transition types (e.g., transitions to the
 syllable $u$) regardless of the social context, indicating that genotype
@@ -993,7 +993,7 @@ duration times.
 
 [The `asthma` data set we use here is from the **SemiMarkov** package
 [@listwon2015semimarkov]. We have renamed and reordered the columns such
-that the data set fits the required format.]{style="color: blue"}
+that the data set fits the required format.]
 Specifically, the data set has $928$ rows, recording the asthma control
 states of $371$ patients, which is one of the following three transient
 states: Optimal control (State 1), sub-optimal control (State 2), and
@@ -1190,9 +1190,9 @@ the package in the future. [Future improvements to the package may
 include more options for the distribution types of transition
 probabilities and duration times beyond the currently available mixture
 Dirichlet and mixture gamma distributions,
-respectively.]{style="color: blue"}
+respectively.]
 
-::: {style="color: blue"}
+::: 
 ## Acknowledgements {#sec:ack}
 
 We thank two anonymous reviewers very much for their careful review of