[Depmix-commits] r377 - papers/jss trunk/R
noreply at r-forge.r-project.org
noreply at r-forge.r-project.org
Thu Mar 4 15:36:56 CET 2010
Author: maarten
Date: 2010-03-04 15:36:55 +0100 (Thu, 04 Mar 2010)
New Revision: 377
Modified:
papers/jss/dpx4Rev.Rnw
trunk/R/makePriorModel.R
Log:
- identity link now default in init models
- minor changes to the jss article
Modified: papers/jss/dpx4Rev.Rnw
===================================================================
--- papers/jss/dpx4Rev.Rnw 2010-03-03 16:09:28 UTC (rev 376)
+++ papers/jss/dpx4Rev.Rnw 2010-03-04 14:36:55 UTC (rev 377)
@@ -308,7 +308,7 @@
For the example data above, $b_j^k$ could be a Gaussian distribution
function for the response time variable, and a Bernoulli distribution
-for the accuracy variable. In the models we are considering here,
+for the accuracy variable. In the models considered here,
both the transition probability functions $a_{ij}$ and the initial
state probability functions $\greekv{\pi}$ may depend on covariates as
well as the response distributions $b_{j}^{k}$.
@@ -488,7 +488,7 @@
these data in the first place.
Response times are a very common dependent variable in psychological
-experiments and hence form the basis for infernce about many
+experiments and hence form the basis for inference about many
psychological processes. A potential threat to such inference based
on response times is formed by the speed-accuracy trade-off: different
participants in an experiment may respond differently to typical
@@ -507,22 +507,22 @@
responding to fast responding at chance level. At each trial of the
experiment, the participant is shown the current setting of the
relative reward for speed versus accuracy. The bottom panel of
-figure~ref{fig:speed} shows the values of this variable. The main
-question in this experiment was what would happen when this reward
-variable would change from reward for accuracy only to reward for
+figure~\ref{fig:speed} shows the values of this variable. The
+experiment was designed to investigate what would happen when this reward
+variable changes from reward for accuracy only to reward for
speed only. The \code{speed} data that we analyse here are from
participant A in Experiment 1 in \citet{Dutilh2010}, who provide a
complete description of the experiment and the relevant theoretical
background.
-The central hypothesis about this data is whether indeed it is best
+The central question regarding this data is whether it is indeed best
described by two modes of responding rather than a single mode of
responding with a continuous trade-off between speed and accuracy.
-The hallmark of having a discontinuity between slow versus speeded
-responding is that the switching between the two modes is assymetric
+The hallmark of a discontinuity between slow versus speeded
+responding is that switching between the two modes is asymmetric
\citep[see e.g.][for a theoretical underpinning of this
claim]{Maas1992}. The \code{fit} help page of \pkg{depmixS4} provides
-a number of examples in which the assymetricity of the switching
+a number of examples in which the asymmetry of the switching
process is tested; those examples and other candidate models are
discussed at length in \citet{Visser2009b}.
@@ -537,7 +537,8 @@
library(depmixS4)
data(speed)
set.seed(1)
-mod <- depmix(response=rt~1, data=speed, nstates=2, trstart=runif(4))
+mod <- depmix(response=rt~1, data=speed, nstates=2,
+ trstart=runif(4))
@
The first line of code loads the \pkg{depmixS4} package and
@@ -555,16 +556,16 @@
\paragraph{Starting values} Note also that start values for the
-transition parameters are provided in this call using the
+transition parameters are provided in this call by the
\code{trstart} argument. At this time, the package does not provide
automatic starting values. Starting values for parameters can be
provided using three arguments: \code{instart} for the parameters
relating to the prior probabilities, \code{trstart}, relating the
transition models, and \code{respstart} for the parameters of the
response models. Note that the starting values for the initial and
-transition models as well as of the multinomial logit response models
+transition models as well as multinomial logit response models
are interpreted as {\em probabilities}, and internally converted to
-multinomial logit parameters.
+multinomial logit parameters (if a logit link function is used).
\paragraph{Fitting the model and printing results} The \code{depmix}
@@ -589,7 +590,7 @@
These statistics can also be extracted using \code{logLik}, \code{AIC}
and \code{BIC}, respectively. By comparison, a 1-state model for
these data, i.e. assuming there is no mixture, has a log-likelihood of
--305.33, and 614.66, and 622.83 for the AIC and BIC respectively.
+$-305.33$, and 614.66, and 622.83 for the AIC and BIC respectively.
Hence, the 2-state model fits the data much better than the 1-state
model. Note that the 1-state model can be specified using \code{mod <-
depmix(rt~1, data=speed, nstates=1)}, although this model is trivial
@@ -610,18 +611,18 @@
\subsection{Covariates on transition parameters}
By default, the transition probabilities and the initial state
-probabilities are parameterized using the multinomial logistic model.
-More precisely, each row of the transition matrix is parameterized by
+probabilities are parameterized using a multinomial model with an
+identity link function.
+Using a multinomial logistic model allows us to include covariates on the
+initial state and transition probabilities. In this case, each row of the
+transition matrix is parameterized by
a baseline category logistic multinomial, meaning that the parameter
for the base category is fixed at zero \citep[see][p.\ 267 ff., for
multinomial logistic models and various
parameterizations]{Agresti2002}. The default baseline category is the
first state. Hence, for example, for a 3-state model, the initial
state probability model would have three parameters of which the first
-is fixed at zero and the other two are freely estimated.
-
-The multinomial logistic model allows us to include covariates on the
-initial state and transition probabilities. \citet{Chung2007} discuss
+is fixed at zero and the other two are freely estimated. \citet{Chung2007} discuss
a related latent transition model for repeated measurement data
($T=2$) using logistic regression on the transition parameters; they
rely on Bayesian methods of estimation. Covariates on the transition
@@ -652,7 +653,7 @@
Multivariate data can be modelled by providing a list of formulae as
well as a list of family objects for the distributions of the various
responses. In above examples we have only used the response times
-which were modelled with the Gaussian distribution. The accuracy
+which were modelled as a Gaussian distribution. The accuracy
variable in the \code{speed} data can be modelled with a multinomial
by specifying the following:
<<>>=
@@ -691,7 +692,7 @@
for these data, we briefly describe them.
The balance scale taks is a famous task for testing cognitive
-strategies developed by Jean Piaget \citep[see]{Siegler1981}.
+strategies developed by Jean Piaget \citep[see][]{Siegler1981}.
Figure~\ref{fig:balance} provides an example of a balance scale item.
Participants' task is to say to which side the balance will tip when
released, or alternatively, whether it will stay in balance. The item
@@ -741,10 +742,10 @@
@
Note here that we define a \code{mix} model instead of a \code{depmix}
-models as these data form independent observations. More formally,
+model as these data form independent observations. More formally,
\code{depmix} models extend the class of \code{mix} models by adding
-the transition models. As for fitting \code{mix} models: as can be
-seen in equation~\ref{eq:Q}, the EM algorithm can be applied by simply
+transition models. As for fitting \code{mix} models: as can be
+seen in Equation~\ref{eq:Q}, the EM algorithm can be applied by simply
dropping the second summand containing the transition parameters, and
this is implemented as such in the EM algorithms in \pkg{depmixS4}.
@@ -813,8 +814,8 @@
(in-)equality constraints. Constraining and fixing parameters is done
using the \code{conpat} argument to the \code{fit}-function, which
specifies for each parameter in the model whether it's fixed (0) or
-free (1 or higher). Equality constraints can be imposed by having two
-parameters have the same number in the \code{conpat} vector. When
+free (1 or higher). Equality constraints can be imposed by giving two
+parameters the same number in the \code{conpat} vector. When
only fixed values are required, the \code{fixed} argument can be used
instead of \code{conpat}, with zeroes for fixed parameters and other
values (ones e.g.) for non-fixed parameters. Fitting the models
@@ -825,7 +826,7 @@
\paragraph{Parameter numbering} When using the \code{conpat} and
\code{fixed} arguments, complete parameter vectors should be supplied,
-i.e., these vectors should have length of the number of parameters of
+i.e., these vectors should have length equal to the number of parameters of
the model, which can be obtained by calling \code{npar(object)}. Note
that this is not the same as the degrees of freedom used e.g.\ in the
\code{logLik} function because \code{npar} also counts the baseline
@@ -901,8 +902,8 @@
\item y: the response variable
\item x: the design matrix, possibly only an intercept
\item paramaters: a named list with the coefficients and possibly
- other parameters, e.g., the standard deviation in the Gaussian
- response model
+ other parameters (e.g., the standard deviation in the Gaussian
+ response model)
\item fixed: a vector of logicals indicating whether parameters are
fixed
\item npar: numerical indicating the number of parameters of the model
@@ -1048,7 +1049,7 @@
for \code{gamlss.distr} for interpretation of these parameters.
After defining all the necessary methods for the new response model,
-we can now define the dependent mixture model using this reponse model.
+we can now define the dependent mixture model using this response model.
The function \code{makeDepmix} is included in \pkg{depmixS4} to have
full control over model specification, and we need it here.
@@ -1086,7 +1087,7 @@
Gaussian in one state and an exgaus distribution in another state.
Note also that according to the AIC and BIC, the model with the exgaus
describes the data much better than the same model in which the
-response times are modeled as gaussian.
+response times are modelled as Gaussian.
\section[Conclusions and future work]{Conclusions \& future work}
@@ -1096,7 +1097,7 @@
also fit latent class regression and finite mixture models, although
it should be noted that more specialized packages are available for
this such as \pkg{FlexMix} \citep{Leisch2004}. The package is
-intended for modeling of (individual) time series data with the aim of
+intended for modelling of (individual) time series data with the aim of
characterizing the transition processes underlying the data. The
possibility to use covariates on the transition matrix greatly
enhances the flexibility of the model. The EM algorithm uses a very
@@ -1114,9 +1115,9 @@
\section*{Acknowledgements}
Ingmar Visser was supported by an EC Framework 6 grant, project 516542
-(NEST). Maarten Speekenbrink was supported by the ESRC Centre for
-Economic Learning and Social Evolution (ELSE). Han van der Maas
-provided the speed-accuracy data \cite{Dutilh2010} and thereby
+(NEST). Maarten Speekenbrink was supported by ESRC grant RES-062-23-1511
+and the ESRC Centre for Economic Learning and Social Evolution (ELSE).
+Han van der Maas provided the speed-accuracy data \cite{Dutilh2010} and thereby
neccessitated implementing models with time-dependent covariates.
Brenda Jansen provided the balance scale data set \citep{Jansen2002}
which was the perfect opportunity to test the covariates on the prior
Modified: trunk/R/makePriorModel.R
===================================================================
--- trunk/R/makePriorModel.R 2010-03-03 16:09:28 UTC (rev 376)
+++ trunk/R/makePriorModel.R 2010-03-04 14:36:55 UTC (rev 377)
@@ -7,7 +7,7 @@
# initial probabilities model, depending on covariates init(=~1 by default)
if(formula==~1) {
- initModel <- transInit(~1,data=data.frame(rep(1,ncases)),nst=nstates,family=multinomial(),pstart=values)
+ initModel <- transInit(~1,data=data.frame(rep(1,ncases)),nst=nstates,family=multinomial(link="identity"),pstart=values)
} else {
if(is.null(data)) {
stop("'Argument initdata missing while the init model is non-trivial")
More information about the depmix-commits
mailing list