# Modelling and Diagnostics of Spatially Autocorrelated Counts

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Spatial Lag Models for Count Data

## 3. Diagnostics

#### 3.1. Non-Randomised Probability Integral Transform

#### 3.2. Scoring Rules

#### 3.3. Relative Deviations Plot

## 4. Monte Carlo Study

#### 4.1. Data Generating Process

#### 4.2. Monte Carlo Results

## 5. Empirical Application

#### 5.1. Data

#### 5.2. Results

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Notes

1 | Proença and Glórias (2021) also employed the SAR-Poisson specification (1), but proposed an alternative two-step Poisson pseudo-maximum likelihood approach to solve the problem of taking logarithms from zero counts. See also Simões et al. (2017), who employed the SAR-Poisson model of Lambert et al. (2016) to analyse the spatial correlation of calls to the Portugese National Healthline. The authors proposed a spatial lag Poisson Bayesian model to be estimated by a suitably augmented Nested Laplace Approximation (INLA) developed by Gómez-Rubio et al. (2015). |

2 | Besag’s model has been used frequently to model spatial heterogeneity in context of a count data model (see, e.g., Gschlößl and Czado 2007; Gschlößl and Czado 2008; Apardian and Smirnov 2020). |

3 | See the very instructive discussion on this in Lambert et al. (2016). |

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**Figure 1.**Observations for the subirth variable in dezils with dark blue representing the lowest values and dark red representing the highest ones.

**Figure 2.**Histogram of start-up firm birth counts in the manufacturing sector, U.S. counties, 2000–2004; x-axis is cut at 100.

**Figure 3.**Estimated conditional expectations. The colours indicate the deciles of the observations, with dark blue representing the lowest values and dark red representing the highest ones (see also Figure 1).

**Table 1.**Simulation results for the Poisson spatial count regression model. BIAS is calculated as the average difference between estimates and true value. RMSE is calculated as the square root of the average squared difference between estimates and the true value.

$\mathit{\rho}\setminus \mathit{n}$ | 100 | 250 | 500 | 1000 | 5000 | 10,000 |
---|---|---|---|---|---|---|

$\mathbf{\rho}$ | ||||||

RMSE | ||||||

0 | 0.0444 | 0.0159 | 0.0141 | 0.0090 | 0.0040 | 0.0023 |

0.2 | 0.0233 | 0.0221 | 0.0210 | 0.0146 | 0.0059 | 0.0041 |

0.4 | 0.0417 | 0.0350 | 0.0205 | 0.0136 | 0.0059 | 0.0044 |

0.6 | 0.0497 | 0.0291 | 0.0175 | 0.0139 | 0.0058 | 0.0038 |

0.8 | 0.0455 | 0.0224 | 0.0152 | 0.0082 | 0.0050 | 0.0043 |

BIAS | ||||||

0 | −0.0034 | −0.0007 | −0.0006 | −0.0002 | 0.0001 | −0.0001 |

0.2 | −0.0009 | −0.0018 | −0.0021 | −0.0016 | −0.0010 | −0.0010 |

0.4 | −0.0040 | −0.0041 | −0.0018 | −0.0015 | −0.0009 | −0.0012 |

0.6 | −0.0048 | −0.0030 | −0.0014 | −0.0010 | −0.0009 | −0.0007 |

0.8 | −0.0113 | −0.0045 | −0.0036 | −0.0030 | −0.0030 | −0.0031 |

${\mathbf{\beta}}_{\mathbf{0}}$ | ||||||

RMSE | ||||||

0 | 0.1493 | 0.0819 | 0.0624 | 0.0425 | 0.0188 | 0.0118 |

0.2 | 0.1174 | 0.0926 | 0.0778 | 0.0560 | 0.0239 | 0.0159 |

0.4 | 0.2378 | 0.1554 | 0.0842 | 0.0628 | 0.0281 | 0.0195 |

0.6 | 0.2951 | 0.1871 | 0.1042 | 0.0900 | 0.0351 | 0.0237 |

0.8 | 0.6341 | 0.2598 | 0.1649 | 0.0732 | 0.0447 | 0.0331 |

BIAS | ||||||

0 | 0.0019 | 0.0012 | 0.0001 | 0.0007 | −0.0011 | 0.0001 |

0.2 | −0.0007 | 0.0045 | 0.0051 | 0.0049 | 0.0040 | 0.0042 |

0.4 | 0.0058 | 0.0103 | 0.0056 | 0.0058 | 0.0047 | 0.0055 |

0.6 | −0.0002 | 0.0083 | 0.0051 | 0.0057 | 0.0062 | 0.0054 |

0.8 | −0.0104 | 0.0026 | 0.0011 | −0.0011 | 0.0027 | 0.0032 |

${\mathbf{\beta}}_{\mathbf{1}}$ | ||||||

RMSE | ||||||

0 | 0.0645 | 0.0422 | 0.0296 | 0.0206 | 0.0093 | 0.0062 |

0.2 | 0.0763 | 0.0426 | 0.0346 | 0.0238 | 0.0107 | 0.0071 |

0.4 | 0.0955 | 0.0569 | 0.0356 | 0.0269 | 0.0114 | 0.0084 |

0.6 | 0.1021 | 0.0704 | 0.0401 | 0.0326 | 0.0130 | 0.0096 |

0.8 | 0.1683 | 0.0844 | 0.0550 | 0.0360 | 0.0173 | 0.0123 |

BIAS | ||||||

0 | −0.0002 | −0.0004 | 0.0002 | −0.0001 | 0.0006 | 0.0001 |

0.2 | 0.0014 | −0.0012 | −0.0005 | −0.0009 | −0.0010 | −0.0007 |

0.4 | −0.0008 | −0.0017 | −0.0012 | −0.0008 | −0.0008 | −0.0009 |

0.6 | −0.0029 | −0.0008 | 0.0001 | −0.0013 | −0.0016 | −0.0006 |

0.8 | 0.0057 | −0.0012 | −0.0003 | 0.0005 | −0.0008 | −0.0008 |

${\mathbf{\beta}}_{\mathbf{2}}$ | ||||||

RMSE | ||||||

0 | 0.0274 | 0.0135 | 0.0119 | 0.0075 | 0.0033 | 0.0021 |

0.2 | 0.0131 | 0.0145 | 0.0140 | 0.0096 | 0.0040 | 0.0027 |

0.4 | 0.0323 | 0.0263 | 0.0141 | 0.0099 | 0.0045 | 0.0029 |

0.6 | 0.0594 | 0.0257 | 0.0149 | 0.0136 | 0.0054 | 0.0037 |

0.8 | 0.1056 | 0.0401 | 0.0254 | 0.0090 | 0.0064 | 0.0046 |

BIAS | ||||||

0 | −0.0006 | −0.0003 | −0.0001 | −0.0001 | 0.0001 | 0.0001 |

0.2 | −0.0003 | −0.0007 | −0.0011 | −0.0008 | −0.0006 | −0.0007 |

0.4 | −0.0013 | −0.0020 | −0.0009 | −0.0011 | −0.0008 | −0.0008 |

0.6 | 0.0008 | −0.0016 | −0.0012 | −0.0009 | −0.0008 | −0.0010 |

0.8 | 0.0023 | −0.0008 | −0.0005 | −0.0001 | −0.0005 | −0.0004 |

**Table 2.**Simulation results for NB spatial count regression model. BIAS is calculated as the average difference between estimates and true value. RMSE is calculated as the square root of the average squared difference between estimates and true value.

$\mathit{\rho}\setminus \mathit{n}$ | 100 | 250 | 500 | 1000 | 5000 | 10,000 |
---|---|---|---|---|---|---|

$\mathbf{\rho}$ | ||||||

RMSE | ||||||

0 | 0.0581 | 0.0352 | 0.0162 | 0.0102 | 0.0041 | 0.0031 |

0.2 | 0.0705 | 0.0438 | 0.0333 | 0.0229 | 0.0125 | 0.0102 |

0.4 | 0.0653 | 0.0580 | 0.0413 | 0.0276 | 0.0148 | 0.0108 |

0.6 | 0.1113 | 0.0652 | 0.0391 | 0.0291 | 0.0129 | 0.0103 |

0.8 | 0.0910 | 0.0539 | 0.0429 | 0.0305 | 0.0129 | 0.0100 |

BIAS | ||||||

0 | −0.0101 | −0.0064 | −0.0009 | −0.0008 | 0.0001 | −0.0001 |

0.2 | −0.0189 | −0.0116 | −0.0103 | −0.0095 | −0.0080 | −0.0079 |

0.4 | −0.0099 | −0.0132 | −0.0129 | −0.0096 | −0.0087 | −0.0074 |

0.6 | −0.0299 | −0.0157 | −0.0087 | −0.0067 | −0.0049 | −0.0054 |

0.8 | −0.0291 | −0.0118 | −0.0108 | −0.0102 | −0.0057 | −0.0056 |

${\mathbf{\beta}}_{\mathbf{0}}$ | ||||||

RMSE | ||||||

0 | 0.2771 | 0.1549 | 0.0990 | 0.0653 | 0.0300 | 0.0196 |

0.2 | 0.3330 | 0.1987 | 0.1498 | 0.1091 | 0.0594 | 0.0493 |

0.4 | 0.3564 | 0.2672 | 0.1868 | 0.1402 | 0.0864 | 0.0706 |

0.6 | 0.7309 | 0.4176 | 0.2675 | 0.1958 | 0.1069 | 0.0908 |

0.8 | 1.2300 | 0.6524 | 0.5012 | 0.3573 | 0.1637 | 0.1334 |

BIAS | ||||||

0 | 0.0142 | 0.0124 | 0.0003 | 0.0017 | −0.0028 | 0.0016 |

0.2 | 0.0581 | 0.0419 | 0.0436 | 0.0460 | 0.0397 | 0.0395 |

0.4 | 0.0481 | 0.0562 | 0.0663 | 0.0617 | 0.0647 | 0.0590 |

0.6 | 0.0836 | 0.0804 | 0.0897 | 0.0761 | 0.0732 | 0.0726 |

0.8 | 0.0421 | 0.0439 | 0.0761 | 0.1181 | 0.0928 | 0.0951 |

${\mathbf{\beta}}_{\mathbf{1}}$ | ||||||

RMSE | ||||||

0 | 0.1297 | 0.0744 | 0.0527 | 0.0373 | 0.0172 | 0.0113 |

0.2 | 0.1598 | 0.0935 | 0.0679 | 0.0470 | 0.0222 | 0.0168 |

0.4 | 0.1734 | 0.1092 | 0.0767 | 0.0560 | 0.0290 | 0.0207 |

0.6 | 0.2461 | 0.1619 | 0.1071 | 0.0761 | 0.0368 | 0.0282 |

0.8 | 0.6660 | 0.2615 | 0.1854 | 0.1267 | 0.0574 | 0.0428 |

BIAS | ||||||

0 | −0.0037 | −0.0024 | −0.0002 | −0.0003 | 0.0018 | −0.0007 |

0.2 | −0.0105 | −0.0078 | −0.0090 | −0.0096 | −0.0078 | −0.0075 |

0.4 | −0.0132 | −0.0126 | −0.0118 | −0.0108 | −0.0140 | −0.0112 |

0.6 | −0.0076 | −0.0132 | −0.0180 | −0.0165 | −0.0164 | −0.0157 |

0.8 | −0.0230 | −0.0058 | −0.0153 | −0.0221 | −0.0200 | −0.0198 |

${\mathbf{\beta}}_{\mathbf{2}}$ | ||||||

RMSE | ||||||

0 | 0.0572 | 0.0363 | 0.0202 | 0.0142 | 0.0061 | 0.0044 |

0.2 | 0.0601 | 0.0397 | 0.0311 | 0.0209 | 0.0118 | 0.0098 |

0.4 | 0.0628 | 0.0520 | 0.0367 | 0.0271 | 0.0163 | 0.0139 |

0.6 | 0.1147 | 0.0784 | 0.0436 | 0.0355 | 0.0195 | 0.0175 |

0.8 | 0.1742 | 0.1007 | 0.0779 | 0.0650 | 0.0278 | 0.0248 |

BIAS | ||||||

0 | −0.0040 | −0.0033 | −0.0004 | −0.0004 | 0.0002 | −0.0003 |

0.2 | −0.0129 | −0.0095 | −0.0094 | −0.0091 | −0.0079 | −0.0079 |

0.4 | −0.0107 | −0.0131 | −0.0142 | −0.0133 | −0.0127 | −0.0121 |

0.6 | −0.0224 | −0.0198 | −0.0171 | −0.0156 | −0.0147 | −0.0146 |

0.8 | −0.0221 | −0.0167 | −0.0166 | −0.0250 | −0.0183 | −0.0198 |

$\mathbf{\alpha}$ | ||||||

RMSE | ||||||

0 | 0.0554 | 0.0358 | 0.0243 | 0.0174 | 0.0075 | 0.0056 |

0.2 | 0.0503 | 0.0314 | 0.0225 | 0.0155 | 0.0077 | 0.0065 |

0.4 | 0.0424 | 0.0295 | 0.0213 | 0.0161 | 0.0098 | 0.0092 |

0.6 | 0.0406 | 0.0256 | 0.0195 | 0.0145 | 0.0095 | 0.0087 |

0.8 | 0.0353 | 0.0227 | 0.0165 | 0.0125 | 0.0079 | 0.0067 |

BIAS | ||||||

0 | −0.0129 | −0.0050 | −0.0028 | −0.0012 | −0.0005 | −0.0002 |

0.2 | −0.0088 | −0.0020 | 0.0004 | 0.0022 | 0.0036 | 0.0042 |

0.4 | −0.0034 | −0.0002 | 0.0056 | 0.0071 | 0.0075 | 0.0081 |

0.6 | 0.0035 | 0.0025 | 0.0082 | 0.0074 | 0.0078 | 0.0077 |

0.8 | −0.0004 | 0.0040 | 0.0046 | 0.0058 | 0.0061 | 0.0056 |

Dependent variable | subirths | Single unit start-ups in the lower 48 United States during 2000–2004 in the manufacturing sector (NAICS 31-33) |

Agglomeration economies | msemp | Manufactoring share of employment |

tfdense | Total establishment density (in 100 s) | |

pel10emp | Percent of manufacturing establishments with less than 10 employees | |

pem100emp | Percent of manufacturing establishments with more than 100 employees | |

Market structure | mhhi | Median household income (in 1000 s) |

pop | Population (in 10,000 s) | |

cclass | Share of workers in creative occupations | |

Labor availability and cost | uer | Unemployment rate |

pedas | Pecent of adults with an associate’s degree | |

avg_wage | Average wage per job (in 1000 s) | |

netflow_emp | Net flow of wages per commuter (in 1000 s) | |

Infrastucture | proad | Public road density |

interst | Interstate highway miles | |

hwy_pc | Government expenditures on highways per capita (in 100 s) | |

avland | Percent of farmland to total county | |

Fiscal policy | educ_pc | Government expenditures on education per capita (in 100 s) |

bci | State tax business climate index (higher values indicate more favorable business climates) | |

Area | metro | Dummy variable indentifying counties as belonging to metropolitan areas |

micro | Dummy variable indentifying counties as belonging to micropolitan areas |

**Table 4.**Estimation results from Poisson and the NB spatial count data regression and the non-spatial Poisson and NB2 regressions. N = 3078; robust standard errors in brackets. ${}^{**}$ and ${}^{***}$ denote a 5% and 1% significance, respectively.

Spatial | Non-Spatial | Spatial | Non-Spatial | ||||||
---|---|---|---|---|---|---|---|---|---|

Variable | Poisson | NB | Poisson | NB2 | Poisson | NB | Poisson | NB2 | |

$\rho $ | 0.288 *** | 0.166 *** | awage | 0.033 *** | −0.058 *** | 0.019 *** | −0.038 *** | ||

(0.043) | (0.022) | (0.008) | (0.012) | (0.007) | (0.007) | ||||

const | −1.707 *** | −1.120 *** | −0.934 *** | −1.066 *** | netflow | 0.003 | −0.027 | 0.002 | −0.016 *** |

(0.397) | (0.249) | (0.281) | (0.195) | (0.003) | (0.006) | (0.820) | (0.003) | ||

msemp | 0.035 *** | 0.053 *** | 0.031 *** | 0.050 *** | proad | 0.093 *** | 0.084 *** | 0.103 *** | 0.083 *** |

(0.006) | (0.003) | (0.004) | (0.002) | (0.023) | (0.024) | (0.018) | (0.022) | ||

pelt10 | −0.007 ** | 0.005 *** | −0.002 | 0.005 *** | interst | 0.009 *** | 0.005 *** | 0.007 *** | 0.005 *** |

(0.003) | (0.001) | (0.002) | (0.001) | (0.001) | (0.001) | (0.001) | (0.001) | ||

pemt100 | −0.034 *** | −0.023 *** | −0.029 *** | −0.018 *** | avland | −0.007 *** | −0.006 *** | −0.009 *** | −0.007 *** |

(0.006) | (0.003) | (0.004) | (0.002) | (0.002) | (0.001) | (0.001) | (0.001) | ||

tfdens | −0.013 | −0.046 *** | 0.006 | −0.053 *** | bci | 0.128 *** | 0.032 | 0.080 | 0.034 |

(0.011) | (0.016) | (0.010) | (0.013) | (0.042) | (0.021) | (0.037) | (0.015) | ||

mhhi | −0.034 *** | 0.024 ** | 0.000 | 0.027 *** | educpc | 0.006 *** | 0.006 ** | 0.004 | 0.004 |

(0.008) | (0.010) | (0.009) | (0.005) | (0.002) | (0.003) | (0.002) | (0.003) | ||

pop | 0.002 *** | 0.017 *** | 0.002 *** | 0.018 *** | hwypc | −0.039 | −0.132 | −0.030 | −0.028 |

(0.000) | (0.003) | (0.000) | (0.003) | (0.023) | (0.031) | (0.019) | (0.021) | ||

cclass | 0.088 *** | 0.101 *** | 0.048 *** | 0.082 *** | metro | 1.630 *** | 1.017 *** | 1.265 *** | 0.845 *** |

(0.011) | (0.007) | (0.013) | (0.005) | (0.157) | (0.081) | (0.092) | (0.054) | ||

uer | 0.037 | 0.076 *** | 0.073 *** | 0.080 *** | micro | 0.839 *** | 0.645 *** | 0.573 *** | 0.546 *** |

(0.037) | (0.021) | (0.022) | (0.013) | (0.119) | (0.055) | (0.063) | (0.038) | ||

pedas | 0.150 *** | 0.062 *** | 0.130 *** | 0.044 *** | $\alpha $ | 0.403 *** | 0.437 *** | ||

(0.022) | (0.011) | (0.021) | (0.009) | (0.026) | (0.024) | ||||

Log L | −28,149 | −10,300 | −32,248 | −10,401 | |||||

logs | 9.002 | 3.348 | 9.917 | 3.379 | |||||

qs | −0.027 | −0.073 | −0.017 | −0.070 | |||||

rps | 14.035 | 22.836 | 15.244 | 33.858 |

**Table 5.**Median of marginal effects of the Poisson and NB spatial count regressions, and the non-spatial Poisson and non-spatial NB2 regressions. For the dummy variables $metro$ and $micro$, the effect of a change from 0 to 1 is given. ${}^{**}$ and ${}^{***}$ denote 5% and 1% significance, respectively. Standard errors (in brackets) were estimated using their sample counterparts of 2000 draws of the asymptotic joint distribution of the coefficients.

Poisson Spatial Reg. | NB Spatial Reg. | Poisson | NB2 | |||||
---|---|---|---|---|---|---|---|---|

Variable | Total M.E. | Direct M.E. | Indirect M.E. | Total M.E. | Direct M.E. | Indirect M.E. | Direct M.E. | Direct M.E. |

msemp | 0.377 *** | 0.198 *** | 0.148 *** | 0.516 *** | 0.339 *** | 0.116 *** | 0.326 *** | 0.463 *** |

(0.061) | (0.040) | (0.032) | (0.032) | (0.026) | (0.018) | (0.044) | (0.024) | |

pelt10 | −0.065 ** | −0.034 ** | −0.025 ** | 0.050 *** | 0.033 *** | 0.011 *** | −0.022 | 0.048 *** |

(0.028) | (0.014) | (0.013) | (0.013) | (0.009) | (0.003) | (0.020) | (0.011) | |

pemt100 | −0.366 *** | −0.192 *** | −0.144 *** | −0.226 *** | −0.148 *** | −0.051 *** | −0.314 *** | −0.171 *** |

(0.062) | (0.035) | (0.035) | (0.034) | (0.021) | (0.012) | (0.038) | (0.023) | |

tfdens | −0.140 | −0.074 | −0.055 | −0.456 *** | −0.299 *** | −0.102 *** | 0.066 | −0.493 *** |

(0.123) | (0.065) | (0.050) | (0.157) | (0.109) | (0.034) | (0.107) | (0.125) | |

mhhi | −0.366 *** | −0.192 *** | −0.144 *** | 0.237 ** | 0.155 ** | 0.053 ** | 0.002 | 0.249 *** |

(0.095) | (0.046) | (0.049) | (0.103) | (0.064) | (0.026) | (0.091) | (0.049) | |

pop | 0.022 *** | 0.011 *** | 0.008 *** | 0.163 *** | 0.107 *** | 0.037 *** | 0.025 *** | 0.170 *** |

(0.005) | (0.003) | (0.002) | (0.033) | (0.023) | (0.008) | (0.005) | (0.030) | |

cclass | 0.948 *** | 0.498 *** | 0.373 *** | 0.987 *** | 0.648 *** | 0.222 *** | 0.516 *** | 0.764 *** |

(0.125) | (0.075) | (0.082) | (0.069) | (0.055) | (0.037) | (0.136) | (0.049) | |

uer | 0.399 | 0.209 | 0.157 | 0.745 *** | 0.489 *** | 0.167 *** | 0.779 *** | 0.750 *** |

(0.398) | (0.212) | (0.159) | (0.215) | (0.133) | (0.059) | (0.236) | (0.124) | |

pedas | 1.616 *** | 0.848 *** | 0.636 *** | 0.608 *** | 0.399 *** | 0.136 *** | 1.387 *** | 0.415 *** |

(0.256) | (0.135) | (0.157) | (0.109) | (0.076) | (0.031) | (0.211) | (0.084) | |

awage | 0.356 *** | 0.187 *** | 0.140 *** | −0.565 *** | −0.371 *** | −0.127 *** | 0.198 *** | −0.354 *** |

(0.089) | (0.047) | (0.044) | (0.129) | (0.072) | (0.040) | (0.075) | (0.062) | |

netflow | 0.032 | 0.017 | 0.013 | −0.267 *** | −0.175 *** | −0.060 *** | 0.025 | −0.146 |

(0.027) | (0.014) | (0.011) | (0.063) | (0.035) | (0.020) | (0.024) | (0.025) | |

proad | 1.002 *** | 0.526 *** | 0.395 *** | 0.825 *** | 0.542 *** | 0.185 *** | 1.097 *** | 0.776 *** |

(0.251) | (0.147) | (0.114) | (0.236) | (0.155) | (0.064) | (0.194) | (0.213) | |

interst | 0.086 *** | 0.045 *** | 0.034 *** | 0.049 *** | 0.032 *** | 0.011 *** | 0.078 *** | 0.044 *** |

(0.014) | (0.008) | (0.008) | (0.009) | (0.006) | (0.003) | (0.011) | (0.007) | |

avland | −0.075 *** | −0.040 *** | −0.030 *** | −0.056 *** | −0.037 *** | −0.013 *** | −0.092 *** | −0.062 *** |

(0.018) | (0.010) | (0.008) | (0.009) | (0.006) | (0.003) | (0.016) | (0.007) | |

bci | 1.368 *** | 0.718 *** | 0.539 *** | 0.313 | 0.206 | 0.070 | 0.855 ** | 0.316 ** |

(0.450) | (0.230) | (0.207) | (0.211) | (0.136) | (0.050) | (0.400) | (0.137) | |

educpc | 0.065 *** | 0.034 *** | 0.025 *** | 0.055 ** | 0.036 ** | 0.012 ** | 0.038 | 0.036 |

(0.022) | (0.012) | (0.010) | (0.025) | (0.017) | (0.006) | (0.020) | (0.025) | |

hwypc | −0.420 | −0.221 | −0.165 | −1.294 *** | −0.850 *** | −0.290 *** | −0.320 | −0.258 |

(0.248) | (0.132) | (0.103) | (0.313) | (0.197) | (0.090) | (0.200) | (0.194) | |

metro | 23.233 *** | 14.520 *** | 7.382 *** | 12.481 *** | 8.632 *** | 2.449 *** | 19.385 *** | 9.909 *** |

(2.972) | (1.486) | (1.791) | (1.304) | (0.752) | (0.513) | (2.288) | (0.822) | |

micro | 10.901 *** | 4.787 *** | 5.031 *** | 7.154 *** | 4.650 *** | 1.757 *** | 6.200 *** | 5.575 *** |

(2.349) | (0.639) | (1.677) | (0.759) | (0.397) | (0.378) | (0.788) | (0.434) |

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## Share and Cite

**MDPI and ACS Style**

Jung, R.C.; Glaser, S.
Modelling and Diagnostics of Spatially Autocorrelated Counts. *Econometrics* **2022**, *10*, 31.
https://doi.org/10.3390/econometrics10030031

**AMA Style**

Jung RC, Glaser S.
Modelling and Diagnostics of Spatially Autocorrelated Counts. *Econometrics*. 2022; 10(3):31.
https://doi.org/10.3390/econometrics10030031

**Chicago/Turabian Style**

Jung, Robert C., and Stephanie Glaser.
2022. "Modelling and Diagnostics of Spatially Autocorrelated Counts" *Econometrics* 10, no. 3: 31.
https://doi.org/10.3390/econometrics10030031