Siena08


The program Siena08

For the meta-analysis of several data sets analyzed by RSiena, the function siena08 can be used.

For SIENA 3, this was the standalone program Siena08. This method may be regarded as a simple kind of multilevel network analysis (where the simplicity refers to the lack of a random coefficient multilevel model).
The method is described in Snijders and Baerveldt (2003), and some applications of Fisher's method of combining independent p-values have been added, as described in the RSiena manual in Section 11, Multilevel network analysis. A set of transparencies explaining this method can be downloaded here, but the manual is more extensive.

Earlier versions of the RSiena function siena08 contained an error in the reported two-sided p-value for the estimated mean parameter. This was corrected (2011-02-05 R-forge revision 134); use the most recent version!



The rest of this page is only relevant for remaining users of Siena 3, because it refers to the standalone program Siena08 which now is superseded by the siena08 function in RSiena.

From this page you can download the version of Siena08 of September 21, 2009. This is a small modification of the April 2008 version, with small improvements in output.
The April 2008 version was a small modification of the December 2007 version, suitable also for Siena versions 3.15 and up.

New in the December 2007 version compared to the version of June 25, 2007:

  • If the SIENA outputs analyzed also include score tests (for ML) or score-type tests (for MoM), then these can also be combined with the Fisher method explained below. The number of score (or score-type) tests must be given in the .mli file (see the example .mli file in the zipped file below).
New in the 2006/2007 version:
  • Error corrected in the August 2006 version which sometimes (rarely) led to a program error.
  • A correction of the standard error for the first estimation stage
    (not an important error in the earlier version because this is something we never use...).
  • A plot of standard errors versus estimates;
    this is important for two reasons:
    1. it allows to see easily how many positive and negative individually significant parameter values are contained in the combined data set;
    2. an assumption of the Snijders-Baerveldt (2003) method for meta-analysis is that estimated standard errors and estimated parameter values are uncorrelated; this can be visually checked from this plot.
  • An extra method for combining the various classes, which does not make this assumption, and which does not make the assumption that the networks are a sample from a population.
    This method is based on Fisher's method for combining independent p-values. It is a double test:
    1. for detecting if there are any networks with a positive parameter value, the null hypothesis tested is
      H0: For all networks, the value of this parameter is zero or less than zero;
      with the alternative hypothesis
      H1: For at least one network, the value of this parameter is greater than zero;
    2. for detecting if there are any networks with a negative parameter value, the null hypothesis tested is
      H0: For all networks, the value of this parameter is zero or greater than zero;
      with the alternative hypothesis
      H1: For at least one network, the value of this parameter is less than zero.
    For each of these combined tests, the p-value is given. It is advisable to use for each the significance level of alpha/2 (e.g., 0.025 if alpha = 0.05) which yields an overall combined test at significance level alpha.
    Note that four different overall results are possible. Indicating the right-sided and the left-sided p-values by p_r and p_l, respectively, these possible results are (">=" means "greater than or equal to"):
    1. p_r >   alpha/2, p_l >   alpha/2:   No evidence for any nonzero parameter values;
    2. p_r <= alpha/2, p_l >   alpha/2:   Evidence that some networks have a positive parameter value, no evidence for any negative parameter values;
    3. p_r >   alpha/2, p_l <= alpha/2:   Evidence that some networks have a negative parameter value, no evidence for any positive parameter values;
    4. p_r <= alpha/2, p_l <= alpha/2:   Evidence that some networks have a negative parameter value, and some others have a positive parameter value.
    If all networks have a zero parameter value, then the probability of result (1) is less than or equal to alpha.
The .mli file is a bit different from the 2007 and earlier version; when you look at the .mli file in the zipped file below, you see immediately how it has to be made.

Download zipped file containing source, executable, and example input files.

Siena08 works on the basis of t-tests (t-ratio = estimate divided by standard error). There may be reasons to distrust t-tests for estimates which are large with also a large standard error. (This is known as the Donner-Hauck phenomenon in logistic regression.) Unfortunately, it is impossible to say in general what is to be regarded as a large standard error.
I propose to work in most cases with a threshold of 4 for the standard error; if a tested parameter has a standard error larger than 4, then it is advisable to redo the analysis in a specification where this parameter only is fixed to 0 and a score test is carried out for this parameter. However, for some effects, in any case for the "average similarity" effect for behavior dynamics, parameters and standard errors tend to be larger, and a larger threshold (e.g. 10) is appropriate. The same holds for effects of covariates with small variances (less than 1).
The result of the score test can be added as follows to the Fisher-combination results of Siena08:

  1. if the one-step estimate is positive, calculate c_r = -2*ln(0.5*p) and c_l = -2*ln(1 - 0.5*p) where p is the p-value obtained for the score test;
    (the "*" symbol denotes multiplication)
    (it may be noted that these are chi-squared values with d.f. = 2);
  2. if the one-step estimate is negative, calculate c_r = -2*ln(1.0 - 0.5*p) and c_l = -2*ln(0.5*p) where p is the p-value obtained for the score test;
  3. add c_r to the right-sided chi-squared value and c_l to the left-sided chi-square value reported by Siena08;
  4. these are again chi-squared values, but the degrees of freedom are 2 higher.
A disadvantage of this procedure is that if there are two or more tested parameters having large standard errors, this procedure including the estimation must be carried out SEPARATELY for each tested parameter, because in testing each parameter you wish to control for all other effects and therefore not fix any other effects to 0.



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