[Rsiena-commits] r165 - pkg/RSienaTest/doc
noreply at r-forge.r-project.org
noreply at r-forge.r-project.org
Thu Jul 28 10:49:48 CEST 2011
Author: tomsnijders
Date: 2011-07-28 10:49:47 +0200 (Thu, 28 Jul 2011)
New Revision: 165
Modified:
pkg/RSienaTest/doc/RSiena.bib
pkg/RSienaTest/doc/RSiena_Manual.tex
Log:
Only RSiena_Manual.tex and RSIena.bib were changed. Many corrections; added sections on user-defined behaviour interactions and uponly/downonly; added pieces about creation effects.
Modified: pkg/RSienaTest/doc/RSiena.bib
===================================================================
--- pkg/RSienaTest/doc/RSiena.bib 2011-07-27 13:19:00 UTC (rev 164)
+++ pkg/RSienaTest/doc/RSiena.bib 2011-07-28 08:49:47 UTC (rev 165)
@@ -8,6 +8,17 @@
pages = {1981--2014}
}
+ at article{AgneessensRoose08,
+ Author = {Filip Agneessens and Henk Roose},
+ Title = {Local structural properties and attribute characteristics in 2-mode
+ networks: $p^*$ models to map choices of theater events},
+ Journal = {Journal of Mathematical Sociology},
+ Volume = {32},
+ Number = {3},
+ Pages = {204--237},
+ Year = {2008} }
+
+
@Article{AlbertAnderson84,
author = {A. Albert and J. A. Anderson},
title = {On the existence of the maximum likelihood estimates
@@ -1774,17 +1785,19 @@
volume = 1,
pages = {49--80}}
+
@ARTICLE{Lospinoso2011,
TITLE={Assessing and Accounting for Time Heterogeneity in Stochastic Actor
Oriented Models},
AUTHOR={Joshua A. Lospinoso and M. Schweinberger and T. A. B. Snijders and
R.M. Ripley},
JOURNAL={Advances in Data Analysis and Computation},
- VOLUME={Special Issue on Social Networks},
YEAR={2011},
doi = {DOI: 10.1016/j.socnet.2010.03.001},
URL = {http://www.stats.ox.ac.uk/~lospinos}
-}
+ volume = 5,
+ pages = {147--176}}
+
@Article{Lospinoso2011b,
TITLE = {Goodness of Fit for Stochastic Actor Oriented Models},
AUTHOR = {Joshua A. Lospinoso and Tom A.B. Snijders},
@@ -1793,6 +1806,18 @@
URL = {http://www.stats.ox.ac.uk/~lospinos}
}
+
+ at Article{Lospinoso2010b,
+ TITLE = {Testing and Modeling Time Heterogeneity in Longitudinal Studies of
+Social Networks: A Tutorial in RSiena},
+ AUTHOR = {Joshua A. Lospinoso},
+ JOURNAL = {Connections},
+ VOLUME = {In progress.},
+ YEAR = {2010},
+ URL = {http://www.stats.ox.ac.uk/~lospinos}
+}
+
+
@InCollection{Lepkowski89,
author = {J. M. Lepkowski},
title = {Treatment of wave nonresponse in panel surveys.},
@@ -1965,6 +1990,21 @@
pages = {824--827}}
+ at article{MischePattison2000,
+title = "Composing a civic arena: Publics, projects, and social settings",
+journal = "Poetics",
+volume = "27",
+number = "2-3",
+pages = "163 - 194",
+year = "2000",
+note = "Relational analysis and institutional meanings: Formal models for the study of culture",
+issn = "0304-422X",
+doi = "DOI: 10.1016/S0304-422X(99)00024-8",
+url = "http://www.sciencedirect.com/science/article/pii/S0304422X99000248",
+author = "Ann Mische and Philippa Pattison"
+}
+
+
@article{MischeWhite98,
Author = {A. Mische and H. White},
Title = { Between Conversation and Situation:
@@ -2176,6 +2216,20 @@
+ at article {PattisonWasserman99,
+ author = {Pattison, Philippa and Wasserman, Stanley},
+ title = {Logit models and logistic regressions for social networks:
+ {I}{I}. Multivariate relations},
+ journal = {British Journal of Mathematical and Statistical Psychology},
+ volume = {52},
+ number = {2},
+ publisher = {Blackwell Publishing Ltd},
+ issn = {2044-8317},
+ url = {http://dx.doi.org/10.1348/000711099159053},
+ doi = {10.1348/000711099159053},
+ pages = {169--193},
+ year = {1999},
+}
@article{
PattisonEA00,
@@ -2362,8 +2416,17 @@
Pages = {457--465},
Year = {1969} }
+ at Manual{R,
+ title = {R: A Language and Environment for Statistical
+ Computing},
+ author = {{R Development Core Team}},
+ organization = {R Foundation for Statistical Computing},
+ address = {Vienna, Austria},
+ year = 2011,
+ note = {{ISBN} 3-900051-07-0},
+ url = {http://www.R-project.org}
+ }
-
@Article{Rao47,
author = {C. R. Rao},
title = {Large sample tests of statistical hypothesis concerning
@@ -2457,12 +2520,12 @@
- at Techreport{SienaManual10,
+ at Techreport{SienaManual11,
Title={Manual for {Siena} version 4.0},
Author={Ruth M. Ripley and Tom A. B. Snijders},
Institution={Oxford: University of Oxford, Department of Statistics;
Nuffield College},
- Year={2010},
+ Year={2011},
url = {http://www.stats.ox.ac.uk/siena/}
}
@@ -2904,8 +2967,8 @@
pages = {567--588}}
@Article{SLT2011,
- title = {Multiplex dynamics of one-mode and two-mode networks,
- with an application to friendship and employment preference},
+ title = {Multiplex dynamics of two-mode and one-mode networks,
+ with an application to employment preference and friendship},
year = {2011},
author = {Tom A. B. Snijders and Alessandro Lomi and Vanina Torl\`{o}},
note = {(submitted)}
@@ -2965,6 +3028,25 @@
volume =14,
pages = {75 -- 100}}
+
+
+
+ at article{Snijders2011,
+author = {Snijders, Tom A.B.},
+title = {Statistical Models for Social Networks},
+journal = {Annual Review of Sociology},
+volume = {37},
+number = {1},
+pages = {131-153},
+year = {2011},
+doi = {10.1146/annurev.soc.012809.102709},
+URL = {http://www.annualreviews.org/doi/abs/10.1146/annurev.soc.012809.102709},
+eprint = {http://www.annualreviews.org/doi/pdf/10.1146/annurev.soc.012809.102709}
+}
+
+
+
+
@article{
SomerfieldEA02,
Author = {Somerfield, P. J. and Clarke, K. R. and Olsgard, F.},
Modified: pkg/RSienaTest/doc/RSiena_Manual.tex
===================================================================
--- pkg/RSienaTest/doc/RSiena_Manual.tex 2011-07-27 13:19:00 UTC (rev 164)
+++ pkg/RSienaTest/doc/RSiena_Manual.tex 2011-07-28 08:49:47 UTC (rev 165)
@@ -674,7 +674,7 @@
\item Install \Rn.
\item Install (within \Rn) the package \rs, and
possibly \sfn{network} (required to read Pajek files), \sfn{snow} and
- \sfn{rlecuyer} (required to use multiple processors).
+ \sfn{rlecuyer} (required to use multiple processes).
\item Set the working directory of \R appropriately (\sfn{setwd()} within \Rn
or via a desktop shortcut).
\item You can get help by the command
@@ -724,7 +724,7 @@
and \sfn{includeInteraction()} to further specify the model.
\item Use \sfn{sienaModelCreate()} to create a model object.
\item Use \sfn{siena07()} to run the estimation procedure.
-\item Note that it is possible to use multiple processors in \sfn{siena07}. For
+\item Note that it is possible to use multiple processes in \sfn{siena07}. For
details see section~\ref{S_multipleProcesses}.
\item Also note the availability of the parameter \sfn{prevAns} to reuse
estimates and derivatives from a previous run with similar effects.
@@ -857,7 +857,7 @@
\label{S_multipleProcesses}
\begin{enumerate}
\item
-If multiple processors are available, then using
+If multiple processes are available, then using
multiple processes can speed up the estimation in \sfn{siena07}.
\item In Phases 1 and 3 the simulations are performed in parallel. In Phase 2,
@@ -869,7 +869,7 @@
\item The parameters required to run all processes on one computer are fairly
simple: in your call to \sfn{siena07}, set \sfn{nbrNodes} to the number of
processes and \sfn{useCluster} and \sfn{initC} to TRUE. The \sfn{Model
- Options} screen also allows you to specify the number of processors, and
+ Options} screen also allows you to specify the number of processes, and
will automatically set the other required parameters for you.
\item To use more than one machine is more complicated, but it can be done by
@@ -1038,7 +1038,6 @@
files with digraphs} are required: the observed networks, one for
each time point. The number of time points is denoted $M$.
-
In addition, various kinds of variables are allowed:
\begin{enumerate}
@@ -1047,7 +1046,8 @@
which can be symbolized as $v_i$ for each actor $i$;
these can be constant over time or changing; \\
the changing individual variables can be dependent variables
- (changing dynamically in mutual dependence with the changing network)
+ (changing dynamically in mutual dependence with the changing network;
+ then they are also called dependent behavior variables)
or independent variables (exogenously changing variables;
then they are also called individual covariates).
\item {\em dyadic covariates}, which can be symbolized as $w_{ij}$
@@ -1060,6 +1060,8 @@
these likewise can be constant over time or changing.
\end{enumerate}
+Dependent variables (which can be networks or behavior variables)
+all must be available for the same set of time points.
All variables must be available in ASCII (`raw text') data files, described in
detail below. It is best to use the `classical' type of filenames, without embedded blanks
@@ -1134,10 +1136,11 @@
Missing values must be indicated in the way usual for \Rn,
by \texttt{NA}.
+For data specification by the graphical interface \textsf{siena01Gui}
+or by the function \textsf{sienaDataCreateFromSession},
+instead of \texttt{NA} any numerical code can be used
+given that this is indicated to be a missing value code.
-
-
-
Although this section talks only about digraphs (directed graphs), it is
also possible that all observed ties (for all time points) are mutual.
This will be automatically detected by \si, and
@@ -1149,6 +1152,8 @@
(In other words, in the simulations of the actor-based model
the actors have only the option to create new ties or to retain
the status quo, not to delete existing ties.)
+Similarly if ties never are created (but only terminated),
+then this will be respected in the simulations.
\subsubsection{Transformation between matrix and edge list formats}
@@ -1158,17 +1163,30 @@
can be used to create the corresponding edge list,
called \texttt{edges} here.
\begin{verbatim}
- # create indicator matrix
+ # create indicator matrix of non-zero entries of a
ones <- !a %in% 0
# create empty edge list of desired length
- edges <- matrix(NA, sum(ones), 3)
+ edges <- matrix(0, sum(ones), 3)
# fill the columns of the edge list
- edges[,1] <- row(a)[ones]
- edges[,2] <- col(a)[ones]
- edges[,3] <- a[ones]
+ edges[, 1] <- row(a)[ones]
+ edges[, 2] <- col(a)[ones]
+ edges[, 3] <- a[ones]
# if desired, order edge list by senders and then receivers
- edges <- edges[order(edges[, 1], edges[, 2]), ]
+ edges <- edges[order(edges[, 1], edges[, 2]), ]
\end{verbatim}
+Some notes on the commands used here:\\
+These commands can be used not only if the adjacency matrix
+contains only 0 and 1 entries, but also if it contains values
+\texttt{NA}, 10, or 11. The possibility of \texttt{NA}
+entries requires special attention;
+\texttt{\%in\%}
+does just what we need, as it quietly says that
+\texttt{NA}'s are not \texttt{\%in\%}
+anything, returning \texttt{FALSE}, which is transformed to
+\texttt{TRUE} by the \texttt{!} function.
+The edge list is created having all 0 values and at the end
+should have no 0 values at all.
+
It is more efficient, however, to work with sparse matrices;
this also is done internally in \rs.
Using the \texttt{Matrix} package for sparse matrix manipulations,
@@ -1178,10 +1196,11 @@
tmp <- as(Matrix(a), "dgTMatrix")
edges2 <- cbind(tmp at i + 1, tmp at j + 1, tmp at x)
\end{verbatim}
-Similarly, if \texttt{edges} is an edge list, then the following commands
+Conversely, if \texttt{edges} is an edge list, then the following commands
can be used to create the corresponding
adjacency matrix, called \texttt{adj},
-with $n$ nodes.
+with $n$ nodes. (For a bipartite network the two dimensions
+will normally be distinct numbers.)
\begin{verbatim}
# create empty adjacency matrix
adj <- matrix(0, n, n)
@@ -1625,102 +1644,231 @@
%The dependent network variable is not centered.
+\subsection{Monotone dependent variables}
+
+In some data sets, a dependent variable only increases, or only decreases.
+For a network, this means that ties can be created but not terminated,
+or the other way around.
+This will be noted by \RS and mentioned in the output file generated by
+\textsf{print01Report}.
+This constraint then is also respected in the simulations. This is represented
+internally by a variable called \texttt{uponly} indicating that the
+dependent variable cannot decrease,
+and a variable \texttt{downonly} indicating that the
+dependent variable cannot increase.
+
+In such cases, the outdegree effect for a dependent network variable,
+and the linear shape effect for a dependent behavior variable (these effects
+are defined below), are not identified and should be dropped from the
+model specification.
+
+
\newpage
\section{Model specification}
\label{S_modspec}
-After defining the data, the next step is to specify a model.\medskip
+\subsection{Definition of the model}
+\label{S_defmod}
-The model specification consists of a selection of `effects' for
-the evolution of each dependent variable (network or behavior).
-% A
-% list of all available effects for a given \SI project is given in
-% the secondary output file \textsf{{\em pname}.log}.
-% A list of all effects in the objective function is given in
-% the file \textsf{{\em pname}.eff}.
+After defining the data, the next step is to specify a model.
+The model specification consists of a selection of `effects'
+for the evolution of each dependent variable (network or behavior).
+To understand this, first a brief review of the definition of the
+actor-oriented model is given
+\citep*[for further explanations see][]{Snijders01, Snijders05,
+SnijdersEA07, SnijdersEA10b}.
-For the longitudinal case, three types of
-effects are distinguished \citep*[see][]{Snijders01, SnijdersEA10b}:
+The model is based on four functions, which first are explained in an
+intuitive way.
+These functions depend on the actor (hence the name `actor-oriented')
+and on the state of the network, behavior, and covariates.
+All these functions are constituted by a weighted sum
+of so-called \emph{effects}, which define the characteristics of
+the network (and behavior, if this is included as a dependent variable)
+that determine the probabilities of changes.
+
\begin{itemize}
-\item {\em rate function effects}\\
+\item {\em rate function}\\
The rate function models the speed by which the dependent variable
changes; more precisely: the speed by which each network actor
gets an opportunity for changing her score on the dependent
variable.\\
Advice: in most cases, start modeling with a constant rate function without
-additional rate function effects. Constant rate functions are
-selected by exclusively checking the `basic rate parameter' (for
-network evolution) and the main rate effects (for behavioral
-evolution) on the {\sf model specification} screen.
+additional rate function effects.
(When there are important size or activity differences between
actors, it is possible that different advice must be given,
and it may be necessary to let the rate function
depend on the individual covariate that indicates this size;
or on the out-degree.)
-%See XXXXXXX.
-\item {\em evaluation function effects}\\
+\item {\em evaluation function }\\
The evaluation function\footnote{The evaluation function was called
\emph{objective function} in \citet{Snijders01}.}
-models the network actors' satisfaction with their local
+is the primary determinant of the probabilities of changes.
+Probabilities are higher for moving towards states with a higher value
+of the evaluation function.
+One way of representing this is that the evaluation function
+models the actor's `satisfaction'\footnote{The term
+`satisfaction' should be interpreted here in a very loose sense;
+the satisfaction interpretation is not necessary at all, but it does give
+a convenient intuitive way of thinking about the model.}
+with her/his local
network neighborhood configuration. It is assumed that actors
change their scores on the dependent variable such that they
improve their total satisfaction -- with a random element
to represent the limited predictability of behavior.
-In contrast to the endowment
-function (described below), the evaluation function evaluates only
+In contrast to the creation and endowment
+functions (described below), the evaluation function evaluates only
the local network neighborhood configuration that results from the
-change under consideration.
+change under consideration, without considering `where you come from'.
In most applications, the evaluation function will
be the main focus of model selection.\\
-The network evaluation function normally should always contain the
-`density', or `out-degree' effect, to account for the observed
-density. For directed networks,
-it mostly is also advisable to include the reciprocity
-effect, this being one of the most fundamental network effects.
-Likewise, behavior evaluation functions should normally always
-contain the shape parameter, to account for the observed
-prevalence of the behavior, and
-(unless the behavior is dichotomous) the quadratic shape effect,
-to account more precisely for the distribution of the behavior.
-\item {\em endowment function effects}\\
-The endowment
-function\footnote{The endowment function is similar to the {\it gratification
-function} in \citet{Snijders01}.} is an extension of the evaluation
-function that allows to distinguish between new and old network
+\item {\em creation function }\\
+The creation function\footnote{A special case of the {\it gratification
+function} in \citet{Snijders01}.}
+distinguishes between new and old network
ties (when evaluating possible network changes) and between
increasing or decreasing behavioral scores (when evaluating
-possible behavioral changes). The function models the loss of
-satisfaction incurred when existing network ties are dissolved or
-when behavioral scores
-are decreased to a lower value (hence the label `endowment').\\
-For a number of effects, the endowment function is implemented
-not for the Method of Moments estimation method,
-but only for Maximum Likelihood and Bayesian estimation.
-This is indicated in Section~\ref{S_math}.\\
-Advice: start modeling without any endowment effects,
-and add them at a later stage.
-Do not use endowment effects for behavior unless
-the behavior variable is dichotomous.
+possible behavioral changes).
+It is a component of the probabilities of change only for changes in
+an upward direction: creation of new ties, augmentation of values
+of the behavior dependent variable.\\
+In the interpretation using satisfaction, the creation function
+models the gain in satisfaction incurred when network ties are created
+or behavioral scores are increased.\\
+\item {\em endowment function}\\
+The endowment function\footnote{The endowment function also is
+a special case of the {\it gratification function} in \citet{Snijders01}.}
+also distinguishes between new and old network
+ties (when evaluating possible network changes) and between
+increasing or decreasing behavioral scores (when evaluating
+possible behavioral changes).
+It is a component of the probabilities of change only for changes in
+a downward direction: termination of existing ties, decrease of values
+of the behavior dependent variable.\\
+In the interpretation using satisfaction, the endowment function
+models the loss in satisfaction incurred when network ties are dissolved or
+behavioral scores are decreased (hence the label `endowment').
\end{itemize}
-The estimation and simulation procedures of \SI operate on the basis
-of the model specification which comprises the set of
-effects included in the model as described above,
-together with the current
-parameter values.
-% and the Model Type
-%(see Section~\ref{S_modeltype}).
-After data input, the constant rate
-parameters and the density effect in the network evaluation function
-have default initial values, depending on the data. All other
-parameter values initially are 0. The estimation process changes
-the current value of the parameters to the estimated values.
-Values of effects not included in the model are not changed by the
-estimation process. It is possible for the user to change
-parameter values and to request that some of the parameters are
-fixed in the estimation process at their current value.
+Leaving aside the rate effects, a given effect can normally be included
+in the model in any of the three `types' or `roles' of
+evaluation, creation, or endowment effect.
+In almost all cases, the advice is to
+start modeling without any creation or endowment effects,
+and add them perhaps at a later stage.
+For example, if the network dynamics in a given data set is such
+that ties mainly are created, and they are dissolved rather rarely,
+then the data will contain little information about the question whether
+creating ties follows different rules than dissolving ties,
+and if one would try to include creation or endowment effects
+for effects already included in the evaluation function,
+this would lead to large standard errors.
+Creation and endowment effects for behavior for behavior variables with more
+than 2 values are still under investigation, and their interpretation
+for practical research still is uncertain.
+A model specification with only evaluation effects and without creation and
+endowment effects leads to exactly the same network dynamics as a specification
+where these effects are turned into creation and endowment effects,
+with the same parameters.
+For any given effect, normally it makes no sense to include the effect
+in all three roles: evaluation, creation, endowment.
+If one wishes to go beyond evaluation effects, then the user has to choose
+between adding an effect in either the creation or the endowment role.
+
+\subsubsection{Mathematical specification}
+\label{S_mathmod}
+
+To attach precise meaning to the intuitive explanations above,
+the mathematical definition of the model is given as follows.
+To keep notation simple, we leave all statistical parameters out of the
+formulae. To keep the section short, we do not give a lot of explanation,
+but refer to the mentioned literature for that purpose.
+
+As explained in \citet*{SnijdersEA10b}, the model is a continuous-time
+Markov chain, and represents how the network (and behavior) has changed
+in small steps (the so-called \emph{ministeps}) from one observed
+to a later observed value. Each ministep entails a change in only
+one tie value, or one behavioral variable, and is modeled as follows.
+
+First consider the network dynamics.
+At any given moment, let the network be denoted $x^0$.
+The rate function for actor $i$ is denoted $\lambda_i(x)$;
+the evaluation function is $f_i(x)$; the creation function is $c_i(x)$;
+and the endowment function is $g_i(x)$.
+
+At any given moment, let the current network be denoted $x^0$.
+The time duration until the next opportunity of change
+is exponentially distributed with parameter
+\[
+ \lambda_+(x^0) \,=\, \sum_i \lambda_i(x^0) \ .
+\]
+This means that the expected time duration is
+\[
+ \frac{1}{\lambda_+(x^0)} \ .
+\]
+The probability that actor $i$ will be the next to
+have an opportunity for change is
+\[
+ \frac{\lambda_i(x^0)}{\lambda_+(x^0)} \ .
+\]
+Now suppose that actor $i$ is the one who has the next opportunity
+for change; one could say, this is the focal actor.
+Actor $i$ then has the possibility to change one network tie,
+or to keep the network as it is.
+Denote by $\mathcal C$ the set of all networks that can be obtained
+as a result.
+Then the probability of the network obtained from this step depends on
+something called the objective function $u_i(x^0, x)$ which will be defined
+in a moment.
+The probability that the next network is $x$ is given by
+\[
+ \frac{\exp(u_i(x^0, x)\big)}
+ {\sum_{x' \in \mathcal C} \exp\big(u_i(x^0, x')\big)} \ .
+\]
+The numerator is required to make all probabilities for this step sum to 1.
+
+The objective function is defined as follows.
+If there is only an evaluation function (mathematically, this means that
+the creation and endowment functions are 0), then
+the objective function is equal to the evaluation function for the new state,
+\[
+ u_i(x^0, x) \,=\, f_i(x) \ .
+\]
+Because of the properties of the exponential function one can just as
+well use define the objective function as the gain in evaluation function,
+\[
+ u_i(x^0, x) \,=\, f_i(x) - f_i(x^0) \ .
+\]
+To define the general case, note that if $x^0$ and $x$ are not the same,
+then they differ in only one tie variable $x_{ij}$.
+Define $\Delta^+(x^0, x) = 1$ if $x$ has one tie more than $x^0$,
+meaning that a tie is created by this change, and $\Delta^+(x^0, x) = 0$
+otherwise.
+Similarly, define $\Delta^-(x^0, x) = 1$ if $x$ has one tie less than $x^0$,
+meaning that a tie is dissolved by this change, and $\Delta^-(x^0, x) = 0$
+otherwise.
+Then the general definition of the objective function is
+\[
+ u_i(x^0, x) \,=\, \big(f_i(x) - f_i(x^0)\big)
+ \,+\, \Delta^+(x^0, x)\,\big(c_i(x) - c_i(x^0)\big)
+ \,+\, \Delta^-(x^0, x)\,\big(g_i(x) - g_i(x^0)\big) \ .
+\]
+This shows that the change in creation function plays a role
+only if a tie is created ($\Delta^+(x^0,x) = 1$), and the change in
+endowment function plays a role
+only if a tie is dissolved ($\Delta^-(x^0,x) = 1$).
+\medskip
+
+For behavior dynamics the definitions are analogous.
+Here a basic assumption is that, when there is an opportunity for change,
+the possible new values for the behavior variable are the current
+value, this value + 1, and this value --1, as long as these changes
+do not take the value out of the permitted range.
+More elaborate explanations are in
+\citep*{SnijdersEA07, SnijdersEA10b, SteglichEA10}.
+
\subsection{Important structural effects for network dynamics:
\protect\newline one-mode networks}
\label{S_imp_str1}
@@ -1991,7 +2139,7 @@
\item the covariate's effect on the rate of network change of the
actor;
\end{enumerate}
-\item {\em network evaluation and endowment functions}
+\item {\em network evaluation, creation, and endowment functions}
\begin{enumerate}
\item the covariate-similarity effect, which is suitable for variables
measured on an interval scale (or at least an ordinal scale
@@ -2048,7 +2196,7 @@
\end{itemize}
The usual order of importance of these covariate effects on
network evolution is: evaluation effects are most important, followed
-by endowment and rate effects. Inside the group of evaluation
+by creation, endowment and rate effects. Inside the group of evaluation
effects, for variables measured on an interval scale
(or ordinal scale with reasonable numerical values),
it is the covariate-similarity effect that is most
@@ -2076,7 +2224,7 @@
For each dyadic covariate, the following network evaluation effects
can be included in the model for network evolution:
\begin{itemize}
-\item {\em network evaluation and endowment functions}
+\item {\em network evaluation, creation, and endowment functions}
\begin{enumerate}
\item main effect of the dyadic covariate;
\item the interaction
@@ -2369,7 +2517,7 @@
tendency function $\xi$ (indicated in the output as \emph{xi}) and
the volatility function $\nu$ (indicated as \emph{nu}). Which new
tie to create, or which existing tie to withdraw, depends in the
-usual way on the evaluation and endowment functions. Thus, the
+usual way on the evaluation, creation, and endowment functions. Thus, the
outdegree distribution is governed by parameters that are not
connected to the parameters for the structural dynamics. The use of
such an approach in statistical modeling minimizes the influence of
@@ -2438,7 +2586,7 @@
For this purpose, Model Type 6 can be chosen,
while for one or more network effects such as the effects
representing transitivity, the null hypothesis is tested that their
-coefficients are zero (see Section~\ref{S_gof}).
+coefficients are zero (see Section~\ref{S_test}).
\fi
@@ -2502,18 +2650,23 @@
\label{S_int_eff}
It is possible for the user to define additional interaction effects for the
-network. % and the behavior.
+network and the behavior.
The basis is provided by the initial definition, by \si, of `unspecified
-interaction effects'. Modifying two or three of the columns named `effect1',
-`effect2', and `effect3' of the effects dataframe
-allows the definition of two-way
-or three-way interactions. The \emph{effectNumber} of the effects between which
-an interaction is required should be entered in the `effect1' and `effect2',
-and for three-way effects, the `effect3' columns. The interaction effect must
-also be `included', but the underlying effects need only be `included' if
+interaction effects'.
+The interaction is defined by
+the columns \texttt{effect1} and \texttt{effect2},
+and for three-way effects, \texttt{effect3},
+in the effects object; they contain the \texttt{effectNumber}
+of the effects that are interacting.
+The interaction effect must also be `included',
+but the underlying effects need only be `included' if
they are also required individually.
-\sfn{includeInteraction} is an \R function provided to facilitate the definition
+One way to specify an interaction is to take one of the unspecified
+interaction effects, work directly on these columns,
+and set the \texttt{include} value to \texttt{TRUE};
+but it is more convenient to work with \sfn{includeInteraction},
+an \R function provided to facilitate the definition
of interaction effects. Such effects can be specified simply by short names and
the names of any variables required to identify the underlying effects: it is
not necessary to know the effectNumbers of the effects. (The effectNumbers would
@@ -2526,7 +2679,8 @@
Alternatively a new version of this list can be displayed in a browser by using
the function:
-\verb|effectsDocumentation()|
+\verb|effectsDocumentation()| \\
+Section~\ref{S_math} of this manual also gives the short names of all effects.
\subsubsection{Interaction effects for network dynamics}
@@ -2537,9 +2691,15 @@
Ego effects of actor variables can interact with all effects.
\item[b.] Dyadic effects can interact with each other.
\end{description}
-(The column ``InteractionType'' in the effects data frame indicates which
-effects are `ego' effects and which are `dyadic' effects.)
-
+Whether an effect is an ego effect or a dyadic effect is defined by
+the column \texttt{interactionType} in the effects data frame.
+You can see the values of the \texttt{interactionType} by requesting,
+if the network variable is called, e.g., \texttt{friendship}, the following:
+\begin{verbatim}
+cbind(myeff[myeff$name=="friendship","effectName"],
+ myeff[myeff$name=="friendship","shortName"],
+ myeff[myeff$name=="friendship","interactionType"])
+\end{verbatim}
Thus a two-way interaction must be between two dyadic effects or between one
ego effect and another effect. A three-way interaction may be between three
dyadic effects, two dyadic effects and an ego effect, or two ego effects and
@@ -2548,8 +2708,8 @@
All effects used in interactions must be defined on the same network
(in the role of dependent variable): that for
which the ``unspecified
-interaction effects'' is defined. And either all must be evaluation effects or
-all must be endowment effects.
+interaction effects'' is defined. And either all must be
+of the same type (evaluation, endowment, or creation effects).
\iffalse
b. Further, interaction effects are permitted
@@ -2861,16 +3021,19 @@
for code \texttt{1003def} between actors $i$ and $j$,
for \texttt{2003def} between actors $i$ and $h$,
for \texttt{3003def} between actors $j$ and $h$, and
-for \texttt{4003def} by the product of the similarity between actors $i$ and $h$
+for \texttt{4003def} by the product of the similarity
+between actors $i$ and $h$
and the similarity between actors $j$ and $h$.
-Analogously, the parameter \texttt{11003def}, \texttt{12003def}, \texttt{13003def},
+Analogously, the parameter \texttt{11003def}, \texttt{12003def},
+\texttt{13003def},
and \texttt{14003def},
specifies transitive triplet effects where the transitive triplet
is weighted by dyadic variable number \textsf{def}:
for code \texttt{11003def} for actors $i$ and $j$,
for \texttt{12003def} for actors $i$ and $h$, and
for \texttt{13003def} for actors $j$ and $h$, and
-for \texttt{14003def} by the product of the dyadic variable for actors $i$ and $h$
+for \texttt{14003def} by the product of the
+dyadic variable for actors $i$ and $h$
and for actors $j$ and $h$.
The dyadic variables here are not centered!!
For example, for the first actor variable,
@@ -2885,69 +3048,133 @@
have the value 1 on a dyadic covariate.
This is achieved by the following codes:
\begin{description}
-\item[\texttt{8003def}]\ : \ transitive triplets restricted to triplets of actors
- having the same value on actor covariate number \texttt{def};
+\item[\texttt{8003def}]\ : \ transitive triplets
+ restricted to triplets of actors
+ having the same value on actor
+ covariate number \texttt{def};
\item[\texttt{8005def}]\ : \ 3-cycles restricted to triplets of actors
- having the same value on actor covariate number \texttt{def};
+ having the same value
+ on actor covariate number \texttt{def};
\item[\texttt{8006def}]\ : \ transitive ties restricted to triplets of actors
[TRUNCATED]
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svnlook diff /svnroot/rsiena -r 165
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