Pith. sign in

REVIEW 1 major objections 4 minor 115 references

An R package unifies spatio-temporal autoregression for means and for dispersion, enabling space-time GARCH and overdispersed counts at fixed sites.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

T0 review · grok-4.5

2026-07-10 10:11 UTC pith:IBNIDUP2

load-bearing objection Solid software paper that ships a usable double-GLM layer for space-time data; the mean models are mostly consolidation, the dispersion extension is the real addition, and the low-mean Poisson bias is documented rather than hidden. the 1 major comments →

arxiv 2607.08276 v1 pith:IBNIDUP2 submitted 2026-07-09 stat.CO stat.ME

glmSTARMA -- An R-Package for fitting autoregressive spatio-temporal models following generalized linear models

Steffen Maletz , Konstantinos Fokianos , Roland Fried This is my paper
classification stat.CO stat.ME MSC 62M1062J1262H11
keywords spatio-temporal modelsdouble generalized linear modelscount time seriesspace-time GARCHdispersion modellingSTARMAR package
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper presents glmSTARMA, an R package that fits autoregressive models to data observed at fixed locations over time when the spatial dependence structure does not change. It uses the language of generalized linear models so that the conditional mean of continuous or discrete responses can depend on past observations, past conditional means, and covariates. Its distinctive claim is that the same apparatus can be applied to the dispersion parameters of the marginal distributions, turning the model into a double generalized linear model. That single extension yields space-time volatility processes (GARCH-type) and count models that can carry over- or under-dispersion that itself evolves over space and time. Estimation, simulation, inference and prediction are all provided, and two data examples (rotavirus incidence and Pacific sea-surface temperature anomalies) demonstrate the workflow.

Core claim

By embedding spatial lag operators inside double generalized linear models, both the conditional mean and the dispersion of a multivariate time series at fixed sites can be given the same autoregressive structure; the resulting framework recovers classical STARMA, space-time GARCH and overdispersed count models as special cases and supplies the accompanying estimation and prediction routines.

What carries the argument

Double generalized linear models with spatial weight matrices: a linear predictor for the mean (built from lagged means, lagged observations and covariates) is paired with an analogous linear predictor for the dispersion, the latter driven by deviance or Pearson pseudo-observations; quasi-maximum likelihood is iterated between the two blocks under stationarity constraints.

Load-bearing premise

The Gamma approximation that turns residuals into pseudo-observations for the dispersion model is treated as accurate enough for estimation, yet for Poisson-type margins it systematically underestimates dispersion dynamics unless the typical count level is already large.

What would settle it

Simulate count series with known spatio-temporal overdispersion at moderate mean levels (well below 35) and check whether the fitted dispersion autoregressive coefficients recover the true values or remain biased downward as predicted by the paper’s own Appendix D.

Watch this falsifier — get emailed when new claim-graph text bears on it.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

1 major / 4 minor

Summary. The manuscript presents the R package glmSTARMA for fitting autoregressive spatio-temporal models at fixed locations with time-invariant spatial weights, using a double generalized linear model (DGLM) framework. Conditional means follow a STARMA-type linear predictor (Eqs. 2/6) with past observations, lagged feedback, and covariates under exponential-dispersion margins and various links (Table 2). A parallel model (Eq. 8) is specified for the dispersion process via deviance or Pearson pseudo-observations, enabling space-time GARCH-type volatility and over-/underdispersion for counts. Estimation uses iterative quasi-maximum likelihood (Algorithm 1) with sandwich standard errors, stability constraints, simulation via copulas, and information criteria; two real-data examples (rotavirus counts, Pacific SST anomalies) and extensive simulations (Appendix D) illustrate the tools.

Significance. If the implementation is correct, the package fills a genuine gap: no existing R package jointly models spatio-temporal mean and dispersion under a unified GLM-style interface for both continuous and discrete responses. The double-GLM layer, sandwich inference, copula-based simulation, and public CRAN/GitHub code are concrete contributions that unify PSTARMA, softplus, STARMA-GARCH and related models and make them usable for high-dimensional spatial count and volatility series. The authors document rather than conceal the low-mean Poisson approximation issue, which strengthens rather than weakens the software claim.

major comments (1)
  1. Remark 1 and Appendix D establish that the Gamma approximation for deviance/Pearson pseudo-observations systematically underestimates autoregressive dispersion parameters for Poisson-type margins unless the unconditional mean is large (around 35). This is a known, regime-dependent limitation of one use-case rather than a load-bearing flaw in the package architecture or the QMLE construction; continuous and high-mean regimes work as advertised. The manuscript already flags the issue, so no structural change is required, but a short practical recommendation (e.g., prefer negative-binomial margins or constant-dispersion quasi-Poisson when means are low) would help applied users.
minor comments (4)
  1. Table 2 and the surrounding text: the softplus/softclipping hyper-parameter c is mentioned but its default and sensitivity are not illustrated; a one-sentence note or small simulation would clarify practical use.
  2. Section 6.2 / Listing 4: the directed neighborhood matrices violate the row-normalization W1=1 assumed earlier; the authors note the effect is negligible, but a brief remark on how the software handles non-row-normalized weights would prevent user confusion.
  3. Appendix A.1: the stability condition (A-1) is presented as a conjecture; citing the univariate GARCH/INGARCH literature more explicitly would strengthen the heuristic.
  4. Minor typos: “caputuring” (p. 29), “disperson” (Algorithm 1), and occasional missing spaces after commas in the LaTeX source.

Circularity Check

0 steps flagged

No significant circularity; package implements and unifies prior DGLM/STARMA frameworks with standard QMLE, documenting known approximation limits rather than deriving results by construction from fitted inputs.

full rationale

This is a software/methods paper whose central contribution is the glmSTARMA R package implementing autoregressive spatio-temporal mean and dispersion models via double GLMs (Smyth 1989) with spatial lagging (Pfeifer & Deutsch 1980). The estimation (iterative QMLE, Algorithm 1, sandwich variance via empirical G and H matrices) follows standard quasi-likelihood construction for exponential dispersion families and does not reduce any claimed prediction or first-principles result to a fitted constant by definition. Self-citations (Maletz et al. 2024 on PSTARMA, related count models) supply background model classes that are independently published and used only as building blocks; they are not invoked as uniqueness theorems that force the present results, nor do they smuggle an ansatz that becomes the paper's claim. Simulation and data examples illustrate the implemented functions; the Gamma approximation for pseudo-observations (Remark 1, Appendix D) is explicitly flagged as regime-dependent (underestimation of AR dispersion parameters for low-mean Poisson-type margins) rather than hidden or re-labeled a prediction. Stability heuristics (A-1) and asymptotic conjectures are presented as such, not as derived theorems circularly dependent on the package outputs. No self-definitional loops, fitted-input-as-prediction, or renaming of known empirical patterns appear in the derivation chain. Score 1 reflects only routine self-citation of prior work by overlapping authors that is not load-bearing for the software claim.

Axiom & Free-Parameter Ledger

3 free parameters · 4 axioms · 0 invented entities

As a statistical-software paper the load-bearing content rests on standard exponential-dispersion-family and quasi-likelihood theory plus a small number of modeling conventions (row-normalized spatial weights, Gamma approximation for pseudo-observations, stability constraints). No new physical entities are postulated; free parameters are the usual regression coefficients estimated from data.

free parameters (3)
  • mean-model coefficients (δ, α_iℓ, β_jℓ, γ_kℓ)
    Estimated by QMLE from the observed series; their values are data-dependent and enter all subsequent inference and prediction.
  • dispersion-model coefficients (δ̃, α̃_iℓ, β̃_jℓ, γ̃_kℓ)
    Likewise estimated iteratively from deviance/Pearson pseudo-observations; central to the double-GLM claim.
  • softplus/softclipping hyper-parameter c
    User-chosen constant (default 1) that controls the degree of linearity of the link; affects the feasible parameter region.
axioms (4)
  • domain assumption Conditional distributions belong to the exponential dispersion family with variance function V(μ) and dispersion ϕ
    Stated in Section 2, equation (1); required for the quasi-likelihood and deviance residuals.
  • domain assumption Spatial weight matrices are row-normalized and neighborhoods of different orders are disjoint
    Section 2.1; used both for theoretical stability heuristics and for practical estimation.
  • domain assumption Deviance (or Pearson) residuals are approximately Gamma(shape=1/2) or scaled χ², justifying the dispersion QMLE
    Remark 1 and Smyth (1989); the paper notes the approximation quality depends on mean level.
  • ad hoc to paper Stability condition ∑|α|+∑|β|<1 (or the softplus variant) guarantees stationarity/ergodicity
    Conjectured in Appendix A.1 by analogy with univariate GARCH/INGARCH; not rigorously proved for the joint mean-dispersion multivariate case.

pith-pipeline@v1.1.0-grok45 · 45697 in / 2759 out tokens · 29275 ms · 2026-07-10T10:11:37.396724+00:00 · methodology

0 comments
read the original abstract

The R package glmSTARMA implements autoregressive models for spatio-temporal data at fixed locations, with time-invariant spatial dependency structure. We rely on generalized linear models methodology and unify several approaches for the analysis of spatial count time series. Such models allow the (conditional) mean of the response to depend on past observations, lagged (conditional) expectations, and covariates. The response can be a continuous or a discrete random variable. Additionally, the package develops inference for double generalized linear models, allowing the dispersion parameter(s) of the marginal distributions to be modeled similarly to the mean process. This is a new capability which introduces, for example, spatio-temporal volatility models, such as space-time GARCH processes, and count time series models with spatio-temporal overdispersion and underdispersion. We provide functions for model estimation, simulation, inference, and prediction. Its use is illustrated by data examples.

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

115 extracted references · 115 canonical work pages · 3 internal anchors

  1. [1]

    Non-Uniform Random Variate Generation , rights =

    Devroye, Luc , urldate =. Non-Uniform Random Variate Generation , rights =. doi:10.1007/978-1-4613-8643-8 , publisher =

    work page doi:10.1007/978-1-4613-8643-8

  2. [2]

    and Thas, O

    Clement, L. and Thas, O. and Vanrolleghem, P.A. and Ottoy, J.P. , urldate =. Spatio-temporal statistical models for river monitoring networks , volume =. doi:10.2166/wst.2006.002 , abstract =

    work page doi:10.2166/wst.2006.002 2006

  3. [3]

    Spatiotemporal analysis of German real-estate prices , volume =

    Otto, Philipp and Schmid, Wolfgang , urldate =. Spatiotemporal analysis of German real-estate prices , volume =. doi:10.1007/s00168-016-0789-y , pages =

    work page doi:10.1007/s00168-016-0789-y

  4. [4]

    and Weiß, Christian H

    Martins, Ana and Scotto, Manuel G. and Weiß, Christian H. and Gouveia, Sónia , urldate =. Space-time integer-valued. doi:10.1214/23-EJS2183 , number =

    work page doi:10.1214/23-ejs2183

  5. [5]

    and Sirmans, C.F

    Pace, R.Kelley and Barry, Ronald and Gilley, Otis W. and Sirmans, C.F. , urldate =. A method for spatial–temporal forecasting with an application to real estate prices , volume =. doi:10.1016/S0169-2070(99)00047-3 , pages =

    work page doi:10.1016/s0169-2070(99)00047-3 2070

  6. [6]

    Space–time modeling of traffic flow , volume =

    Kamarianakis, Yiannis and Prastacos, Poulicos , urldate =. Space–time modeling of traffic flow , volume =. doi:10.1016/j.cageo.2004.05.012 , pages =

    work page doi:10.1016/j.cageo.2004.05.012 2004

  7. [7]

    Spatio-temporal count autoregression , volume =

    Maletz, Steffen and Fokianos, Konstantinos and Fried, Roland , urldate =. Spatio-temporal count autoregression , volume =. doi:10.1080/26941899.2024.2425171 , pages =

    work page doi:10.1080/26941899.2024.2425171 2024

  8. [8]

    Paul and Emili, Silvia , urldate =

    Elhorst, J. Paul and Emili, Silvia , urldate =. A spatial econometric multivariate model of Okun's law , volume =. doi:10.1016/j.regsciurbeco.2021.103756 , pages =

    work page doi:10.1016/j.regsciurbeco.2021.103756 2021

  9. [9]

    Short-term probabilistic forecasting of meso-scale near-surface urban temperature fields , volume =

    Choi, Byeongseong and Bergés, Mario and Bou-Zeid, Elie and Pozzi, Matteo , urldate =. Short-term probabilistic forecasting of meso-scale near-surface urban temperature fields , volume =. doi:10.1016/j.envsoft.2021.105189 , pages =

    work page doi:10.1016/j.envsoft.2021.105189 2021

  10. [10]

    and Dixon, Philip M

    Clark, Nicholas J. and Dixon, Philip M. , urldate =. A class of spatially correlated self-exciting statistical models , volume =. doi:10.1016/j.spasta.2021.100493 , pages =

    work page doi:10.1016/j.spasta.2021.100493 2021

  11. [11]

    A statistical framework for the analysis of multivariate infectious disease surveillance counts , volume =

    Held, Leonhard and Höhle, Michael and Hofmann, Mathias , urldate =. A statistical framework for the analysis of multivariate infectious disease surveillance counts , volume =. doi:10.1191/1471082X05st098oa , abstract =

    work page doi:10.1191/1471082x05st098oa

  12. [12]

    A modelling approach for correcting reporting delays in disease surveillance data , volume =

    Bastos, Leonardo S and Economou, Theodoros and Gomes, Marcelo F C and Villela, Daniel A M and Coelho, Flavio C and Cruz, Oswaldo G and Stoner, Oliver and Bailey, Trevor and Codeço, Claudia T , urldate =. A modelling approach for correcting reporting delays in disease surveillance data , volume =. doi:10.1002/sim.8303 , abstract =

    work page doi:10.1002/sim.8303

  13. [13]

    Assessing the effect of containment measures on the spatio-temporal dynamic of

    Dickson, Maria Michela and Espa, Giuseppe and Giuliani, Diego and Santi, Flavio and Savadori, Lucia , urldate =. Assessing the effect of containment measures on the spatio-temporal dynamic of. doi:10.1007/s11071-020-05853-7 , abstract =

    work page doi:10.1007/s11071-020-05853-7

  14. [14]

    A systematic review of spatio-temporal statistical models: theory, structure, and applications , rights =

    Habereder, Isabella and Kneib, Thomas and Echizen, Isao and Spinde, Timo , urldate =. A systematic review of spatio-temporal statistical models: theory, structure, and applications , rights =. doi:10.48550/ARXIV.2511.00422 , shorttitle =

    work page doi:10.48550/arxiv.2511.00422

  15. [15]

    Udny , urldate =

    Yule, G. Udny , urldate =. Why do we sometimes get nonsense-correlations between time-series?--A study in sampling and the nature of time-series , volume =. doi:10.2307/2341482 , shorttitle =

    work page doi:10.2307/2341482

  16. [16]

    The summation of random causes as the source of cyclic processes , volume =

    Slutzky, Eugen , urldate =. The summation of random causes as the source of cyclic processes , volume =. doi:10.2307/1907241 , pages =

    work page doi:10.2307/1907241

  17. [17]

    A Study In The Analysis Of Stationary Time Series , publisher =

    Wold, Herman , date =. A Study In The Analysis Of Stationary Time Series , publisher =

    work page

  18. [18]

    Box, George E. P. and Jenkins, Gwilym M. , date =. Time Series Analysis: Forecasting and Control , isbn =

    work page

  19. [19]

    Cliff, A. D. and Ord, J. K. , urldate =. Space-time modelling with an application to regional forecasting , issn =. doi:10.2307/621469 , pages =

    work page doi:10.2307/621469

  20. [20]

    Martin, R. L. and Oeppen, J. E. , urldate =. The identification of regional forecasting models using space: time correlation functions , issn =. doi:10.2307/621623 , shorttitle =

    work page doi:10.2307/621623

  21. [21]

    and Deutsch, Stuart Jay , urldate =

    Pfeifer, Phillip E. and Deutsch, Stuart Jay , urldate =. Identification and interpretation of first order space-time. doi:10.1080/00401706.1980.10486172 , pages =

    work page doi:10.1080/00401706.1980.10486172 1980

  22. [22]

    , urldate =

    Deutsch, Stuart Jay and Pfeifer, Phillip E. , urldate =. Space-Time. doi:10.1080/00401706.1981.10487686 , pages =

    work page doi:10.1080/00401706.1981.10487686 1981

  23. [23]

    and Deutsch, Stuart Jay , urldate =

    Pfeifer, Phillip E. and Deutsch, Stuart Jay , urldate =. Variance of the Sample Space-Time Correlation Function of Contemporaneously Correlated Variables , volume =. doi:10.1137/0140010 , pages =

    work page doi:10.1137/0140010

  24. [24]

    and Deutsch, Stuart Jay , urldate =

    Pfeifer, Phillip E. and Deutsch, Stuart Jay , urldate =. A. doi:10.2307/621846 , pages =

    work page doi:10.2307/621846

  25. [25]

    Journal of the Royal Statistical Society Series B: Statistical Methodology , author =

    Pfeifer, Phillip E. and Deutsch, Stuart Jay , urldate =. Variance of the Sample Space-Time Autocorrelation Function , volume =. doi:10.1111/j.2517-6161.1981.tb01144.x , abstract =

    work page doi:10.1111/j.2517-6161.1981.tb01144.x 1981

  26. [26]

    and Deutsch, Stuart Jay , urldate =

    Pfeifer, Phillip E. and Deutsch, Stuart Jay , urldate =. Seasonal Space‐Time. doi:10.1111/j.1538-4632.1981.tb00720.x , pages =

    work page doi:10.1111/j.1538-4632.1981.tb00720.x 1981

  27. [27]

    , urldate =

    Sims, Christopher A. , urldate =. Macroeconomics and Reality , volume =. doi:10.2307/1912017 , pages =

    work page doi:10.2307/1912017

  28. [28]

    Tiao, G. C. and Box, G. E. P. , urldate =. Modeling Multiple Times Series with Applications , volume =. doi:10.2307/2287575 , pages =

    work page doi:10.2307/2287575

  29. [29]

    , date =

    Quenouille, Maurice H. , date =. The Analysis of Multiple Time Series , pagetotal =

    work page

  30. [30]

    Borovkova, Svetlana and Lopuhaa, Rik , urldate =. Spatial. doi:10.2139/ssrn.2176781 , shorttitle =

    work page doi:10.2139/ssrn.2176781

  31. [31]

    A Stationary Spatio‐Temporal

    Hølleland, Sondre and Karlsen, Hans Arnfinn , urldate =. A Stationary Spatio‐Temporal. doi:10.1111/jtsa.12498 , abstract =

    work page doi:10.1111/jtsa.12498

  32. [32]

    Generalised spatial and spatiotemporal autoregressive conditional heteroscedasticity , volume =

    Otto, Philipp and Schmid, Wolfgang and Garthoff, Robert , urldate =. Generalised spatial and spatiotemporal autoregressive conditional heteroscedasticity , volume =. doi:10.1016/j.spasta.2018.07.005 , pages =

    work page doi:10.1016/j.spasta.2018.07.005 2018

  33. [33]

    and Ruchjana, Budi Nurani , urldate =

    Borovkova, Svetlana and Lopuhaä, Hendrik P. and Ruchjana, Budi Nurani , urldate =. Consistency and asymptotic normality of least squares estimators in generalized. doi:10.1111/j.1467-9574.2008.00391.x , abstract =

    work page doi:10.1111/j.1467-9574.2008.00391.x 2008

  34. [34]

    Generalized autoregressive conditional heteroskedasticity , volume =

    Bollerslev, Tim , urldate =. Generalized autoregressive conditional heteroskedasticity , volume =. doi:10.1016/0304-4076(86)90063-1 , pages =

    work page doi:10.1016/0304-4076(86)90063-1

  35. [35]

    Endemic-epidemic models with discrete-time serial interval distributions for infectious disease prediction , volume =

    Bracher, Johannes and Held, Leonhard , urldate =. Endemic-epidemic models with discrete-time serial interval distributions for infectious disease prediction , volume =. doi:10.1016/j.ijforecast.2020.07.002 , pages =

    work page doi:10.1016/j.ijforecast.2020.07.002 2020

  36. [36]

    Al‐Osh, M. A. and Alzaid, A. A. , urldate =. doi:10.1111/j.1467-9892.1987.tb00438.x , abstract =

    work page doi:10.1111/j.1467-9892.1987.tb00438.x 1987

  37. [37]

    doi:10.1111/j.1752-1688.1985.tb05379.x , abstract =

    work page doi:10.1111/j.1752-1688.1985.tb05379.x 1985

  38. [38]

    Approximately linear

    Jahn, Malte and Weiß, Christian H and Kim, Hee-Young , urldate =. Approximately linear. doi:10.1093/jrsssc/qlad018 , abstract =

    work page doi:10.1093/jrsssc/qlad018

  39. [39]

    Integer‐Valued

    Ferland, René and Latour, Alain and Oraichi, Driss , urldate =. Integer‐Valued. doi:10.1111/j.1467-9892.2006.00496.x , abstract =

    work page doi:10.1111/j.1467-9892.2006.00496.x 2006

  40. [40]

    Log-linear Poisson autoregression , volume =

    Fokianos, Konstantinos and Tjøstheim, Dag , urldate =. Log-linear Poisson autoregression , volume =. doi:10.1016/j.jmva.2010.11.002 , pages =

    work page doi:10.1016/j.jmva.2010.11.002 2010

  41. [41]

    Multivariate count autoregression , volume =

    Fokianos, Konstantinos and Støve, Bård and Tjøstheim, Dag and Doukhan, Paul , urldate =. Multivariate count autoregression , volume =. doi:10.3150/19-BEJ1132 , number =

    work page doi:10.3150/19-bej1132

  42. [42]

    Box, G. E. P. and Tiao, G. C. , urldate =. Intervention Analysis with Applications to Economic and Environmental Problems , volume =. doi:10.1080/01621459.1975.10480264 , pages =

    work page doi:10.1080/01621459.1975.10480264 1975

  43. [43]

    Interventions in log-linear Poisson autoregression , volume =

    Fokianos, Konstantinos and Fried, Roland , urldate =. Interventions in log-linear Poisson autoregression , volume =. doi:10.1177/1471082X1201200401 , abstract =

    work page doi:10.1177/1471082x1201200401

  44. [44]

    A negative binomial integer-valued

    Fokianos, Konstantinos and Fried, Roland , urldate =. Interventions in. doi:10.1111/j.1467-9892.2010.00657.x , pages =

    work page doi:10.1111/j.1467-9892.2010.00657.x 2010

  45. [45]

    Spatial Econometrics: Methods and Models , volume =

    Anselin, Luc , urldate =. Spatial Econometrics: Methods and Models , volume =. doi:10.1007/978-94-015-7799-1 , series =

    work page doi:10.1007/978-94-015-7799-1

  46. [46]

    A negative binomial integer-valued

    Zhu, Fukang , urldate =. A negative binomial integer-valued. doi:10.1111/j.1467-9892.2010.00684.x , shorttitle =

    work page doi:10.1111/j.1467-9892.2010.00684.x 2010

  47. [47]

    and Yang, Eunho and Allen, Genevera I

    Inouye, David I. and Yang, Eunho and Allen, Genevera I. and Ravikumar, Pradeep , urldate =. A review of multivariate distributions for count data derived from the Poisson distribution , volume =. doi:10.1002/wics.1398 , abstract =

    work page doi:10.1002/wics.1398

  48. [48]

    Spatial Data Science: With Applications in R , isbn =

    Pebesma, Edzer and Bivand, Roger , urldate =. Spatial Data Science: With Applications in R , isbn =. doi:10.1201/9780429459016 , shorttitle =

    work page doi:10.1201/9780429459016

  49. [49]

    and Zammit Mangion, Andrew and Cressie, Noel A

    Wikle, Christopher K. and Zammit Mangion, Andrew and Cressie, Noel A. C. , date =. Spatio-temporal statistics with R , isbn =

    work page

  50. [50]

    Cressie, Noel A. C. and Wikle, Christopher K. , date =. Statistics for spatio-temporal data , isbn =

    work page

  51. [51]

    spdep: Spatial Dependence: Weighting Schemes, Statistics , url =

    Bivand, Roger , urldate =. spdep: Spatial Dependence: Weighting Schemes, Statistics , url =. doi:10.32614/CRAN.package.spdep , shorttitle =

    work page doi:10.32614/cran.package.spdep

  52. [52]

    Tobler, W. R. , urldate =. A Computer Movie Simulating Urban Growth in the Detroit Region , volume =. doi:10.2307/143141 , pages =

    work page doi:10.2307/143141

  53. [53]

    Network vector autoregression , volume =

    Zhu, Xuening and Pan, Rui and Li, Guodong and Liu, Yuewen and Wang, Hansheng , urldate =. Network vector autoregression , volume =. doi:10.1214/16-AOS1476 , number =

    work page doi:10.1214/16-aos1476

  54. [54]

    An Introduction to Spatial Data Science with

    Anselin, Luc , urldate =. An Introduction to Spatial Data Science with. doi:10.1201/9781003274919 , shorttitle =

    work page doi:10.1201/9781003274919

  55. [55]

    Count network autoregression , volume =

    Armillotta, Mirko and Fokianos, Konstantinos , urldate =. Count network autoregression , volume =. doi:10.1111/jtsa.12728 , abstract =

    work page doi:10.1111/jtsa.12728

  56. [56]

    Nelder, J. A. and Wedderburn, R. W. M. , urldate =. Generalized Linear Models , volume =. doi:10.2307/2344614 , pages =

    work page doi:10.2307/2344614

  57. [57]

    Exponential Dispersion Models , volume =

    Jørgensen, Bent , urldate =. Exponential Dispersion Models , volume =. doi:10.1111/j.2517-6161.1987.tb01685.x , abstract =

    work page doi:10.1111/j.2517-6161.1987.tb01685.x 1987

  58. [58]

    doi:10.32614/CRAN.package.glmSTARMA , shorttitle =

    Maletz, Steffen and Fokianos, Konstantinos and Fried, Roland , urldate =. doi:10.32614/CRAN.package.glmSTARMA , shorttitle =

    work page doi:10.32614/cran.package.glmstarma

  59. [59]

    Barreto‐Souza, Wagner and Piancastelli, Luiza S. C. and Fokianos, Konstantinos and Ombao, Hernando , urldate =. Time‐Varying Dispersion Integer‐Valued. doi:10.1111/jtsa.12838 , abstract =

    work page doi:10.1111/jtsa.12838

  60. [60]

    doi:10.1017/S0266466620000134 , pages =

    Aknouche, Abdelhakim and Francq, Christian , date =. doi:10.1017/S0266466620000134 , pages =

    work page doi:10.1017/s0266466620000134

  61. [61]

    and Deutsch, Stuart Jay , urldate =

    Pfeifer, Phillip E. and Deutsch, Stuart Jay , urldate =. A Three-Stage Iterative Procedure for Space-Time Modeling , volume =. doi:10.2307/1268381 , abstract =

    work page doi:10.2307/1268381

  62. [62]

    Strong Consistency of Maximum Quasi-Likelihood Estimators in Generalized Linear Models with Fixed and Adaptive Designs , volume =

    Chen, Kani and Hu, Inchi and Ying, Zhiliang , urldate =. Strong Consistency of Maximum Quasi-Likelihood Estimators in Generalized Linear Models with Fixed and Adaptive Designs , volume =

    work page

  63. [63]

    Asymptotic Properties of Quasi-Maximum Likelihood Estimates in Generalized Linear Models , volume =

    Zhang, Sanguo and Liao, Yuan and Ning, Wei , urldate =. Asymptotic Properties of Quasi-Maximum Likelihood Estimates in Generalized Linear Models , volume =. doi:10.1080/03610926.2010.513792 , abstract =

    work page doi:10.1080/03610926.2010.513792 2010

  64. [64]

    Asymptotic properties of maximum quasi-likelihood estimators in generalized linear models with adaptive designs , volume =

    Gao, Qi-Bing and Lin, Jin-Guan and Zhu, Chun-Hua and Wu, Yao-Hua , urldate =. Asymptotic properties of maximum quasi-likelihood estimators in generalized linear models with adaptive designs , volume =. doi:10.1080/02331888.2010.543465 , abstract =

    work page doi:10.1080/02331888.2010.543465 2010

  65. [65]

    Asymptotic normality and strong consistency of maximum quasi-likelihood estimates in generalized linear models , volume =

    Yin, Changming and Zhao, Lincheng and Wei, Chengdong , urldate =. Asymptotic normality and strong consistency of maximum quasi-likelihood estimates in generalized linear models , volume =. doi:10.1007/s11425-004-5169-x , abstract =

    work page doi:10.1007/s11425-004-5169-x

  66. [66]

    Francq, Christian and Zakoïan, Jean-Michel , date =

    work page

  67. [67]

    The Annals of Statistics , author =

    Fahrmeir, Ludwig and Kaufmann, Heinz , urldate =. Consistency and Asymptotic Normality of the Maximum Likelihood Estimator in Generalized Linear Models , volume =. doi:10.1214/aos/1176346597 , abstract =

    work page doi:10.1214/aos/1176346597

  68. [68]

    Akaike's Information Criterion in Generalized Estimating Equations , volume =

    Pan, Wei , urldate =. Akaike's Information Criterion in Generalized Estimating Equations , volume =

    work page

  69. [69]

    , urldate =

    Akaike, H. , urldate =. A new look at the statistical model identification , volume =. doi:10.1109/TAC.1974.1100705 , abstract =

    work page doi:10.1109/tac.1974.1100705 1974

  70. [70]

    Schwarz,Estimating the dimension of a model, The annals of statistics, 6 (1978), pp

    Schwarz, Gideon , urldate =. Estimating the Dimension of a Model , volume =. doi:10.1214/aos/1176344136 , abstract =

    work page doi:10.1214/aos/1176344136

  71. [71]

    Algorithm 733:

    Kraft, Dieter , urldate =. Algorithm 733:. doi:10.1145/192115.192124 , shorttitle =

    work page doi:10.1145/192115.192124

  72. [72]

    , date =

    Ypma, Jelma and Johnson, Steven G. , date =. nloptr: R Interface to

    work page

  73. [73]

    , urldate =

    Otto, Philipp and Doğan, Osman and Taşpınar, Süleyman and Schmid, Wolfgang and Bera, Anil K. , urldate =. Spatial and spatiotemporal volatility models: A review , volume =. doi:10.1111/joes.12643 , shorttitle =

    work page doi:10.1111/joes.12643

  74. [74]

    , urldate =

    Stoffer, David S. , urldate =. Estimation and Identification of Space-Time. doi:10.2307/2289008 , abstract =

    work page doi:10.2307/2289008

  75. [75]

    Otto, Philipp , urldate =

    work page

  76. [76]

    , date =

    Wood, Simon N. , date =. Generalized Additive Models: An Introduction with R, Second Edition , isbn =. doi:10.1201/9781315370279 , shorttitle =

    work page doi:10.1201/9781315370279

  77. [77]

    starma: Modelling Space Time

    Cheysson, Felix , date =. starma: Modelling Space Time

    work page

  78. [78]

    Spatio-Temporal Analysis of Epidemic Phenomena Using the R Package surveillance , volume =

    Meyer, Sebastian and Held, Leonhard and Höhle, Michael , urldate =. Spatio-Temporal Analysis of Epidemic Phenomena Using the R Package surveillance , volume =. doi:10.18637/jss.v077.i11 , abstract =

    work page doi:10.18637/jss.v077.i11

  79. [79]

    and Held, L

    Paul, M. and Held, L. and Toschke, A. M. , urldate =. Multivariate modelling of infectious disease surveillance data , volume =. doi:10.1002/sim.3440 , abstract =

    work page doi:10.1002/sim.3440

  80. [81]

    Bivand, Roger and Wong, David W. S. , date =. Comparing implementations of global and local indicators of spatial association , volume =. doi:10.1007/s11749-018-0599-x , pages =

    work page doi:10.1007/s11749-018-0599-x

Showing first 80 references.