The Representation of Social Processes by Markov Models

Singer, Burton H.; Spilerman, Seymour

doi:10.1086/226269

Cited by 222 publications

(137 citation statements)

References 25 publications

Supporting

Mentioning

133

Contrasting

Unclassified

Order By: Relevance

“…The imbedding problem for finite Markov chains has a long history and was first posed by Elfving [5], which has applications to population movements in social science [21], credit ratings in mathematical finance [11], and statistical inference for Markov processes [1,18]. For a review of the imbedding problem, the reader can refer to [2].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

On the Imbedding Problem for Three-State Time Homogeneous Markov Chains with Coinciding Negative Eigenvalues

Chen

2010

J Theor Probab

View full text Add to dashboard Cite

For an indecomposable 3×3 stochastic matrix (i.e., 1-step transition probability matrix) with coinciding negative eigenvalues, a new necessary and sufficient condition of the imbedding problem for time homogeneous Markov chains is shown by means of an alternate parameterization of the transition rate matrix (i.e., intensity matrix, infinitesimal generator), which avoids calculating matrix logarithm or matrix square root. In addition, an implicit description of the imbedding problem for the 3 × 3 stochastic matrix in [13] is pointed out.

show abstract

Section: Introductionmentioning

confidence: 99%

“…By the Runnenberg condition in [21,20], the complex eigenvalue −p + iq of the transition rate matrix Q satisfies that…”

mentioning

confidence: 99%

On the Imbedding Problem for Three-State Time Homogeneous Markov Chains with Coinciding Negative Eigenvalues

Chen

2010

J Theor Probab

View full text Add to dashboard Cite

show abstract

“…The method estimates transition rates from the transition probabilities of the discrete-time Markov chain embedded in the Markov process studied (embedded Markov chain). A similar approach was discussed by Singer and Spilerman (1976). Some methods go beyond Markov processes.…”

Section: Statistical Inferencementioning

confidence: 98%

“…The package uses the maximum likelihood method developed by Kalbfleisch and Lawless (1985) for the analysis of panel data and the application of that theory by Wolf (1986) and Laditka and Wolf (1998). The method is closely related to the inverse method proposed by Singer and Spilerman (1976). Since subjects are observed at discrete points in time, the contribution to the likelihood of pairs of observations given the continuous-time model is the transition probability.…”

Section: Statistical Inferencementioning

confidence: 99%

Software for multistate analysis

Willekens¹,

Putter²

2014

DemRes

View full text Add to dashboard Cite

“…A way of testing whether the p th roots of the transition matrix then, the p th roots of the transition matrix M are stochastic [15]. However, if these conditions are not fulfilled we can still have the case 2) above.…”

Section: On Roots Of Stochastic Matricesmentioning

confidence: 99%

Information mobility in complex networks

Estrada

2009

Phys. Rev. E

View full text Add to dashboard Cite

The concept of information mobility in complex networks is introduced on the basis of a stochastic process taking place in the network. The transition matrix for this process represents the probability that the information arising at a given node is transferred to a target one. We use the fractional powers of this transition matrix to investigate the stochastic process at fractional time intervals. The mobility coefficient is then introduced on the basis of the trace of these fractional powers of the stochastic matrix. The fractional time at which a network diffuses 50% of the information contained in its nodes ( 50 / 1 k ) is also introduced. We then show that the scale-free random networks display better spread of information than the non scale-free ones. We study 38 real-world networks and analyze their performance in spreading information from their nodes. We find that some real-world networks perform even better than the scale-free networks with the same average degree and we point out some of the structural parameters that make this possible.

show abstract

The Representation of Social Processes by Markov Models

Cited by 222 publications

References 25 publications

On the Imbedding Problem for Three-State Time Homogeneous Markov Chains with Coinciding Negative Eigenvalues

On the Imbedding Problem for Three-State Time Homogeneous Markov Chains with Coinciding Negative Eigenvalues

Software for multistate analysis

Information mobility in complex networks

Contact Info

Product

Resources

About