Birds_Maquis_analysis_by_plot
Ron Chen
2023-06-12
## Loading required package: readxl## Loading required package: lubridate##
## Attaching package: 'lubridate'## The following objects are masked from 'package:data.table':
##
## hour, isoweek, mday, minute, month, quarter, second, wday, week,
## yday, year## The following objects are masked from 'package:base':
##
## date, intersect, setdiff, union## Loading required package: solartime## - Winter data excluded.
## - The counts of all passing / wintering species (not resident nor breeding in the sampled unit) were set to zero. Abreed_and_non_breed contains the non-breeders as well.Mediterranean Maquis
Unit is divided into 3 subunits: Judea, Carmel and Galilee. Factors are proximity to settlements and time. Sampling started in spring 2012 (pilot year), but during T0 sampling was performed only in winter of 2014, and the next spring sampling was done in T1 (2015). Therefore 2012 will not be considered as pilot here but as T0. Total 5 campaigns, 3subunits per campaign, 5 sites per subunit, with 6 plots per site (total of 450 plot-campaign combinations).
Raw data Total abundance: 21855 Number of observations: 5795 Total richness: 108
Filtered data Total abundance: 13796 Number of observations: 4265 Total richness: 49
Model gma, abundance and richness
Richness done with rare species. Abundance and mean abundance done without rare species. Full models include cosine and sine of the time difference from June 21st (in radians).
richness
Explore data and plot mean-variance plot. There is a strong relationship, indicating that employing GLMs is the proper way to analyze, rather than OLS (assumption of homogeneity is violated).
## [1] "RICHNESS WITH RARE SPECIES"## ℹ SHA-1 hash of file is "eef55df1963ba201f57cf44513f566298756fd4f"
| richness | year_ct | site | settlements | subunit | td_sc | cos_td_rad | sin_td_rad | h_from_sunrise | cos_hsun | sin_hsun | monitors_name | wind | precipitation | temperature | clouds | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Min. : 0.000 | Min. :0.0 | Nir Etzion : 31 | Far :224 | Judean Highlands:149 | Min. :-1.9882 | Min. :-0.1671 | Min. :-1.0000 | Length:444 | Min. :-0.3289 | Min. :-0.1253 | Sassi Haham : 53 | 0 : 33 | 0 :119 | 0 : 4 | 0 : 32 | |
| 1st Qu.: 6.000 | 1st Qu.:3.0 | Ein Yaakov : 30 | Near:220 | Carmel :150 | 1st Qu.:-0.2713 | 1st Qu.: 0.5702 | 1st Qu.:-0.8215 | Class :difftime | 1st Qu.: 0.6855 | 1st Qu.: 0.2563 | Eyal Shochat: 47 | 1 : 42 | 3 : 2 | 1 : 38 | 1 : 0 | |
| Median : 8.000 | Median :5.0 | Givat Yearim : 30 | NA | Galilee :145 | Median : 0.4918 | Median : 0.8140 | Median :-0.5808 | Mode :numeric | Median : 0.8738 | Median : 0.4863 | Eran Banker : 30 | 2 : 12 | NA’s:323 | 2 : 37 | 2 : 5 | |
| Mean : 8.054 | Mean :4.8 | Givat Yeshayahu: 30 | NA | NA | Mean : 0.3205 | Mean : 0.7098 | Mean :-0.5864 | NA | Mean : 0.7997 | Mean : 0.4836 | Asaf Mayrose: 18 | 3 : 2 | NA | 3 : 18 | 3 : 13 | |
| 3rd Qu.:10.000 | 3rd Qu.:7.0 | Goren : 30 | NA | NA | 3rd Qu.: 1.1023 | 3rd Qu.: 0.9413 | 3rd Qu.:-0.3375 | NA | 3rd Qu.: 0.9666 | 3rd Qu.: 0.7281 | Ohad Sharir : 18 | NA’s:355 | NA | NA’s:347 | NA’s:394 | |
| Max. :18.000 | Max. :9.0 | Kerem Maharal : 30 | NA | NA | Max. : 1.7127 | Max. : 0.9976 | Max. :-0.0688 | NA | Max. : 1.0000 | Max. : 0.9998 | (Other) : 58 | NA | NA | NA | NA | |
| NA | NA | (Other) :263 | NA | NA | NA | NA | NA | NA | NA’s :89 | NA’s :89 | NA’s :220 | NA | NA | NA | NA |
no observation for all 4 weather variables. many NAs for sampling time of day variables.exclude from model. An extreme observation of richness>20 in Judean highlands near settlements.
| richness | year_ct | site | settlements | subunit | td_sc | cos_td_rad | sin_td_rad | h_from_sunrise | cos_hsun | sin_hsun | |
|---|---|---|---|---|---|---|---|---|---|---|---|
| richness | 1.0000000 | -0.0647635 | 0.0926545 | 0.4762118 | -0.1936858 | 0.0617968 | 0.0751315 | 0.0460403 | -0.0582024 | 0.0933868 | -0.0342460 |
| year_ct | -0.0647635 | 1.0000000 | -0.0460962 | -0.0041782 | 0.0046005 | -0.6240340 | -0.5599811 | -0.6642968 | 0.0244310 | -0.0070326 | 0.0341395 |
| site | 0.0926545 | -0.0460962 | 1.0000000 | 0.0038640 | -0.1472070 | 0.0103683 | 0.0017250 | 0.0296647 | -0.0105111 | -0.0092740 | -0.0240278 |
| settlements | 0.4762118 | -0.0041782 | 0.0038640 | 1.0000000 | -0.0167082 | 0.0029695 | 0.0016285 | 0.0037459 | 0.0341209 | -0.0071595 | 0.0507160 |
| subunit | -0.1936858 | 0.0046005 | -0.1472070 | -0.0167082 | 1.0000000 | -0.0056370 | -0.0129685 | -0.0136922 | 0.1193296 | -0.1166460 | 0.1174210 |
| td_sc | 0.0617968 | -0.6240340 | 0.0103683 | 0.0029695 | -0.0056370 | 1.0000000 | 0.9788766 | 0.9693667 | -0.1975082 | 0.1811635 | -0.2043768 |
| cos_td_rad | 0.0751315 | -0.5599811 | 0.0017250 | 0.0016285 | -0.0129685 | 0.9788766 | 1.0000000 | 0.9008724 | -0.1878186 | 0.1700185 | -0.1970275 |
| sin_td_rad | 0.0460403 | -0.6642968 | 0.0296647 | 0.0037459 | -0.0136922 | 0.9693667 | 0.9008724 | 1.0000000 | -0.2005880 | 0.1868900 | -0.2040813 |
| h_from_sunrise | -0.0582024 | 0.0244310 | -0.0105111 | 0.0341209 | 0.1193296 | -0.1975082 | -0.1878186 | -0.2005880 | 1.0000000 | -0.9598144 | 0.9818950 |
| cos_hsun | 0.0933868 | -0.0070326 | -0.0092740 | -0.0071595 | -0.1166460 | 0.1811635 | 0.1700185 | 0.1868900 | -0.9598144 | 1.0000000 | -0.8930078 |
| sin_hsun | -0.0342460 | 0.0341395 | -0.0240278 | 0.0507160 | 0.1174210 | -0.2043768 | -0.1970275 | -0.2040813 | 0.9818950 | -0.8930078 | 1.0000000 |
Fit Poisson glm, check for existence of overdispersion
## [1] "Estimating overdispersion parameter phi: (Res. Dev.)/(n-p) where n=number of observations; p=number of parameters in the model."## [1] "od = 0.911421796551234"Overdispersion parameter is < 1. Choose Poisson.
## Warning in checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, :
## Model failed to converge with max|grad| = 0.00212765 (tol = 0.002, component 1)mixed model failed to converge. check vif.
## GVIF Df GVIF^(1/(2*Df))
## settlements 3.276022 1 1.809979
## year_ct 4.624930 1 2.150565
## subunit 3.299661 2 1.347775
## cos_td_rad 5.685761 1 2.384483
## sin_td_rad 7.452876 1 2.729996
## settlements:year_ct 4.691866 1 2.166072
## year_ct:subunit 7.151841 2 1.635326go with mixed model, attempt model selection yet.
## Generalized linear mixed model fit by maximum likelihood (Laplace
## Approximation) [glmerMod]
## Family: poisson ( log )
## Formula: richness ~ settlements * year_ct + subunit * year_ct + cos_td_rad +
## sin_td_rad + (1 | site)
## Data: P.anal
##
## AIC BIC logLik deviance df.resid
## 2115.9 2161.0 -1047.0 2093.9 433
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.00871 -0.60449 -0.09758 0.58170 2.82777
##
## Random effects:
## Groups Name Variance Std.Dev.
## site (Intercept) 0.008489 0.09213
## Number of obs: 444, groups: site, 16
##
## Fixed effects:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 1.463667 0.217828 6.719 1.83e-11 ***
## settlementsNear 0.394936 0.061558 6.416 1.40e-10 ***
## year_ct 0.002820 0.011532 0.245 0.8068
## subunitCarmel 0.112586 0.093603 1.203 0.2291
## subunitGalilee -0.085175 0.098040 -0.869 0.3850
## cos_td_rad 0.346220 0.151470 2.286 0.0223 *
## sin_td_rad -0.307700 0.178412 -1.725 0.0846 .
## settlementsNear:year_ct -0.002305 0.010856 -0.212 0.8318
## year_ct:subunitCarmel -0.006280 0.012993 -0.483 0.6289
## year_ct:subunitGalilee -0.024484 0.014572 -1.680 0.0929 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) sttlmN yer_ct sbntCr sbntGl cs_td_ sn_td_ sttN:_ yr_c:C
## settlmntsNr -0.178
## year_ct -0.228 0.467
## subunitCrml -0.345 -0.002 0.331
## subunitGall -0.378 0.008 0.310 0.516
## cos_td_rad -0.921 0.009 0.043 0.119 0.155
## sin_td_rad 0.880 -0.011 0.098 -0.168 -0.220 -0.857
## sttlmntsN:_ 0.150 -0.833 -0.560 0.001 -0.008 -0.009 0.012
## yr_ct:sbntC 0.324 0.001 -0.493 -0.660 -0.368 -0.161 0.251 0.002
## yr_ct:sbntG 0.353 -0.008 -0.437 -0.341 -0.688 -0.204 0.298 0.014 0.516
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## Model failed to converge with max|grad| = 0.00212765 (tol = 0.002, component 1)perform stepwise model selection of poisson mixed model.
## Single term deletions
##
## Model:
## richness ~ settlements * year_ct + subunit * year_ct + cos_td_rad +
## sin_td_rad + (1 | site)
## npar AIC
## <none> 2115.9
## cos_td_rad 1 2119.2
## sin_td_rad 1 2116.9
## settlements:year_ct 1 2114.0
## year_ct:subunit 2 2115.0remove settlements X year.
## Warning in checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, :
## Model failed to converge with max|grad| = 0.00233045 (tol = 0.002, component 1)## Warning in checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, :
## Model failed to converge with max|grad| = 0.00227907 (tol = 0.002, component 1)## Warning in checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, :
## Model failed to converge with max|grad| = 0.00284994 (tol = 0.002, component 1)## Single term deletions
##
## Model:
## richness ~ settlements + subunit * year_ct + cos_td_rad + sin_td_rad +
## (1 | site)
## npar AIC
## <none> 2114.0
## settlements 1 2241.6
## cos_td_rad 1 2117.3
## sin_td_rad 1 2114.9
## subunit:year_ct 2 2113.0drop year X subunit.
## Single term deletions
##
## Model:
## richness ~ settlements + subunit + year_ct + cos_td_rad + sin_td_rad +
## (1 | site)
## npar AIC
## <none> 2113.0
## settlements 1 2240.8
## subunit 2 2120.3
## year_ct 1 2111.5
## cos_td_rad 1 2115.1
## sin_td_rad 1 2112.8drop year.
## Single term deletions
##
## Model:
## richness ~ settlements + subunit + cos_td_rad + sin_td_rad +
## (1 | site)
## npar AIC
## <none> 2111.5
## settlements 1 2239.4
## subunit 2 2118.7
## cos_td_rad 1 2113.3
## sin_td_rad 1 2110.8drop sine.
## Single term deletions
##
## Model:
## richness ~ settlements + subunit + cos_td_rad + (1 | site)
## npar AIC
## <none> 2110.8
## settlements 1 2238.5
## subunit 2 2118.0
## cos_td_rad 1 2113.5Settlements, subunit and time of year remain. Final model:
## Generalized linear mixed model fit by maximum likelihood (Laplace
## Approximation) [glmerMod]
## Family: poisson ( log )
## Formula: richness ~ settlements + subunit + cos_td_rad + (1 | site)
## Data: P.anal
##
## AIC BIC logLik deviance df.resid
## 2110.8 2135.4 -1049.4 2098.8 438
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.09026 -0.59675 -0.07933 0.56203 2.96581
##
## Random effects:
## Groups Name Variance Std.Dev.
## site (Intercept) 0.009619 0.09808
## Number of obs: 444, groups: site, 16
##
## Fixed effects:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 1.80687 0.07258 24.896 <2e-16 ***
## settlementsNear 0.38421 0.03401 11.296 <2e-16 ***
## subunitCarmel 0.08257 0.07349 1.124 0.2612
## subunitGalilee -0.20004 0.07405 -2.702 0.0069 **
## cos_td_rad 0.13535 0.06305 2.147 0.0318 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) sttlmN sbntCr sbntGl
## settlmntsNr -0.279
## subunitCrml -0.526 0.002
## subunitGall -0.508 0.009 0.502
## cos_td_rad -0.635 -0.002 0.021 -0.003## $site
## (Intercept)
## Abirim -7.321848e-02
## Aderet 6.137108e-02
## Beit Oren -2.233669e-02
## Ein Yaakov -2.970003e-02
## Givat Yearim -7.623271e-02
## Givat Yeshayahu 9.364091e-02
## Goren -7.232404e-03
## Iftach 1.773011e-01
## Kerem Maharal 9.669359e-02
## Kfar Shamai -5.892993e-02
## Margaliot -1.725282e-03
## Nehusha -4.299542e-02
## Nir Etzion -1.521589e-01
## Ofer 8.260917e-02
## Ramat Raziel -3.076398e-02
## Yagur 2.684868e-05
##
## with conditional variances for "site"## $site
attempt to add year, see if significant:
## Generalized linear mixed model fit by maximum likelihood (Laplace
## Approximation) [glmerMod]
## Family: poisson ( log )
## Formula: richness ~ year_ct + settlements + subunit + cos_td_rad + (1 |
## site)
## Data: P.anal
##
## AIC BIC logLik deviance df.resid
## 2112.8 2141.5 -1049.4 2098.8 437
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.0946 -0.6000 -0.0782 0.5691 2.9651
##
## Random effects:
## Groups Name Variance Std.Dev.
## site (Intercept) 0.009581 0.09788
## Number of obs: 444, groups: site, 16
##
## Fixed effects:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 1.8147139 0.0962891 18.847 <2e-16 ***
## year_ct -0.0008103 0.0065499 -0.124 0.9015
## settlementsNear 0.3841894 0.0340127 11.295 <2e-16 ***
## subunitCarmel 0.0824132 0.0733925 1.123 0.2615
## subunitGalilee -0.2001589 0.0739537 -2.707 0.0068 **
## cos_td_rad 0.1298876 0.0769263 1.688 0.0913 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) yer_ct sttlmN sbntCr sbntGl
## year_ct -0.658
## settlmntsNr -0.214 0.005
## subunitCrml -0.407 0.016 0.002
## subunitGall -0.391 0.013 0.009 0.502
## cos_td_rad -0.769 0.574 0.001 0.027 0.005year not significant, rightfully dropped. center time of year variable, highly correlated with intercept.
## Generalized linear mixed model fit by maximum likelihood (Laplace
## Approximation) [glmerMod]
## Family: poisson ( log )
## Formula: richness ~ settlements + subunit + cos_td_rad_c + (1 | site)
## Data: P.anal
##
## AIC BIC logLik deviance df.resid
## 2110.8 2135.4 -1049.4 2098.8 438
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.09026 -0.59674 -0.07933 0.56201 2.96580
##
## Random effects:
## Groups Name Variance Std.Dev.
## site (Intercept) 0.009619 0.09808
## Number of obs: 444, groups: site, 16
##
## Fixed effects:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 1.90293 0.05611 33.916 <2e-16 ***
## settlementsNear 0.38421 0.03401 11.296 <2e-16 ***
## subunitCarmel 0.08256 0.07349 1.124 0.2612
## subunitGalilee -0.20004 0.07404 -2.702 0.0069 **
## cos_td_rad_c 0.13534 0.06305 2.147 0.0318 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) sttlmN sbntCr sbntGl
## settlmntsNr -0.363
## subunitCrml -0.663 0.002
## subunitGall -0.660 0.009 0.502
## cos_td_rd_c -0.023 -0.002 0.021 -0.003## Registered S3 methods overwritten by 'broom':
## method from
## tidy.glht jtools
## tidy.summary.glht jtools| Observations | 444 |
| Dependent variable | richness |
| Type | Mixed effects generalized linear model |
| Family | poisson |
| Link | log |
| AIC | 2110.815 |
| BIC | 2135.390 |
| Pseudo-R² (fixed effects) | 0.292 |
| Pseudo-R² (total) | 0.345 |
| exp(Est.) | S.E. | z val. | p | |
|---|---|---|---|---|
| (Intercept) | 6.706 | 0.056 | 33.916 | 0.000 |
| settlementsNear | 1.468 | 0.034 | 11.296 | 0.000 |
| subunitCarmel | 1.086 | 0.073 | 1.124 | 0.261 |
| subunitGalilee | 0.819 | 0.074 | -2.702 | 0.007 |
| cos_td_rad_c | 1.145 | 0.063 | 2.147 | 0.032 |
| Group | Parameter | Std. Dev. |
|---|---|---|
| site | (Intercept) | 0.098 |
| Group | # groups | ICC |
|---|---|---|
| site | 16 | 0.010 |
## Confidence intervals for merMod models is an experimental feature. The
## intervals reflect only the variance of the fixed effects, not the random
## effects.
## Confidence intervals for merMod models is an experimental feature. The
## intervals reflect only the variance of the fixed effects, not the random
## effects.
statistically significant lower richness in Galilee and far from settlements. No significant change in richness over time.
Near plots have on average 3.1412275 more species than far plots, which is 46.8453321 percent higher. Galilee plots have on average 1.5043163 less species than Carmel and Judean highland plots, which is 21.50837 percent lower.
geometric mean of abundance
Explore data. Exclude time of day because of high number of NAs.
## [1] "GEOMETRIC MEAN ABUNDANCE WITHOUT RARE SPECIES"
| gma | year_ct | site | settlements | subunit | td_sc | cos_td_rad | sin_td_rad | |
|---|---|---|---|---|---|---|---|---|
| Min. : 0.000 | Min. :0.0 | Nir Etzion : 31 | Far :224 | Judean Highlands:149 | Min. :-1.9882 | Min. :-0.1671 | Min. :-1.0000 | |
| 1st Qu.: 2.075 | 1st Qu.:3.0 | Ein Yaakov : 30 | Near:220 | Carmel :150 | 1st Qu.:-0.2713 | 1st Qu.: 0.5702 | 1st Qu.:-0.8215 | |
| Median : 2.555 | Median :5.0 | Givat Yearim : 30 | NA | Galilee :145 | Median : 0.4918 | Median : 0.8140 | Median :-0.5808 | |
| Mean : 2.811 | Mean :4.8 | Givat Yeshayahu: 30 | NA | NA | Mean : 0.3205 | Mean : 0.7098 | Mean :-0.5864 | |
| 3rd Qu.: 3.252 | 3rd Qu.:7.0 | Goren : 30 | NA | NA | 3rd Qu.: 1.1023 | 3rd Qu.: 0.9413 | 3rd Qu.:-0.3375 | |
| Max. :10.301 | Max. :9.0 | Kerem Maharal : 30 | NA | NA | Max. : 1.7127 | Max. : 0.9976 | Max. :-0.0688 | |
| NA | NA | (Other) :263 | NA | NA | NA | NA | NA |
Fit glm, compare gamma, gaussian (poisson inappropriate because response is not discrete)
Remove rows 211, 376, 408. Fit fixed and mixed models.
Mixed model converged
## Linear mixed model fit by REML ['lmerMod']
## Formula: gma ~ settlements * year_ct + subunit * year_ct + cos_td_rad +
## sin_td_rad + (1 | site)
## Data: P.anal
##
## REML criterion at convergence: 1307.3
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.4491 -0.5895 -0.1466 0.4279 5.7748
##
## Random effects:
## Groups Name Variance Std.Dev.
## site (Intercept) 0.07917 0.2814
## Residual 1.04011 1.0199
## Number of obs: 441, groups: site, 16
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 0.56769 0.62892 0.903
## settlementsNear 0.29906 0.17755 1.684
## year_ct 0.01253 0.03226 0.388
## subunitCarmel 0.39222 0.28413 1.380
## subunitGalilee 0.08268 0.28571 0.289
## cos_td_rad 1.37461 0.43324 3.173
## sin_td_rad -1.79442 0.52429 -3.423
## settlementsNear:year_ct -0.02317 0.03109 -0.745
## year_ct:subunitCarmel -0.05681 0.03928 -1.446
## year_ct:subunitGalilee -0.03377 0.04105 -0.823
##
## Correlation of Fixed Effects:
## (Intr) sttlmN yer_ct sbntCr sbntGl cs_td_ sn_td_ sttN:_ yr_c:C
## settlmntsNr -0.152
## year_ct -0.216 0.402
## subunitCrml -0.361 -0.003 0.341
## subunitGall -0.392 0.007 0.331 0.524
## cos_td_rad -0.922 0.011 0.044 0.130 0.156
## sin_td_rad 0.883 -0.012 0.106 -0.176 -0.219 -0.862
## sttlmntsN:_ 0.129 -0.837 -0.483 0.001 -0.005 -0.011 0.012
## yr_ct:sbntC 0.343 0.000 -0.511 -0.659 -0.368 -0.182 0.266 0.005
## yr_ct:sbntG 0.373 -0.007 -0.482 -0.351 -0.676 -0.214 0.308 0.008 0.533perform stepwise model selection of gaussian model.
## Single term deletions
##
## Model:
## gma ~ settlements * year_ct + subunit * year_ct + cos_td_rad +
## sin_td_rad + (1 | site)
## npar AIC
## <none> 1300.3
## cos_td_rad 1 1308.3
## sin_td_rad 1 1310.2
## settlements:year_ct 1 1298.8
## year_ct:subunit 2 1298.4drop year * subunit
## Single term deletions
##
## Model:
## gma ~ settlements * year_ct + subunit + cos_td_rad + sin_td_rad +
## (1 | site)
## npar AIC
## <none> 1298.4
## subunit 2 1295.5
## cos_td_rad 1 1305.3
## sin_td_rad 1 1306.9
## settlements:year_ct 1 1296.9drop subunit
## Single term deletions
##
## Model:
## gma ~ settlements * year_ct + cos_td_rad + sin_td_rad + (1 |
## site)
## npar AIC
## <none> 1295.5
## cos_td_rad 1 1302.3
## sin_td_rad 1 1304.0
## settlements:year_ct 1 1294.0drop year*settlements
## Single term deletions
##
## Model:
## gma ~ settlements + year_ct + cos_td_rad + sin_td_rad + (1 |
## site)
## npar AIC
## <none> 1294.0
## settlements 1 1295.9
## year_ct 1 1293.3
## cos_td_rad 1 1300.8
## sin_td_rad 1 1302.5drop year.
## Single term deletions
##
## Model:
## gma ~ settlements + cos_td_rad + sin_td_rad + (1 | site)
## npar AIC
## <none> 1293.3
## settlements 1 1295.1
## cos_td_rad 1 1299.3
## sin_td_rad 1 1300.7drop settlements.
## Single term deletions
##
## Model:
## gma ~ cos_td_rad + sin_td_rad + (1 | site)
## npar AIC
## <none> 1295.1
## cos_td_rad 1 1301.1
## sin_td_rad 1 1302.3Only time of year remains. This is the final model:
## Linear mixed model fit by REML ['lmerMod']
## Formula: gma ~ cos_td_rad + sin_td_rad + (1 | site)
## Data: P.anal
##
## REML criterion at convergence: 1289.7
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.1686 -0.6028 -0.1680 0.4155 5.9316
##
## Random effects:
## Groups Name Variance Std.Dev.
## site (Intercept) 0.07121 0.2668
## Residual 1.04627 1.0229
## Number of obs: 441, groups: site, 16
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 1.1366 0.5452 2.085
## cos_td_rad 1.1853 0.4181 2.835
## sin_td_rad -1.3341 0.4381 -3.045
##
## Correlation of Fixed Effects:
## (Intr) cs_td_
## cos_td_rad -0.968
## sin_td_rad 0.960 -0.903
Not a great fit. None of the factors of interest (year, subunit, settlements) are significant.
| Observations | 441 |
| Dependent variable | gma |
| Type | Mixed effects linear regression |
| AIC | 1299.67 |
| BIC | 1320.12 |
| Pseudo-R² (fixed effects) | 0.02 |
| Pseudo-R² (total) | 0.08 |
| Est. | S.E. | t val. | d.f. | p | |
|---|---|---|---|---|---|
| (Intercept) | 1.14 | 0.55 | 2.07 | 407.53 | 0.04 |
| cos_td_rad | 1.19 | 0.42 | 2.81 | 429.81 | 0.01 |
| sin_td_rad | -1.33 | 0.44 | -3.02 | 418.77 | 0.00 |
| p values calculated using Kenward-Roger standard errors and d.f. |
| Group | Parameter | Std. Dev. |
|---|---|---|
| site | (Intercept) | 0.27 |
| Residual | 1.02 |
| Group | # groups | ICC |
|---|---|---|
| site | 16 | 0.06 |
abundance
Explore data
## [1] "ABUNDANCE WITHOUT RARE SPECIES"
| abundance | year_ct | site | settlements | subunit | td_sc | cos_td_rad | sin_td_rad | |
|---|---|---|---|---|---|---|---|---|
| Min. : 0.00 | Min. :0.0 | Nir Etzion : 31 | Far :224 | Judean Highlands:149 | Min. :-1.9882 | Min. :-0.1671 | Min. :-1.0000 | |
| 1st Qu.: 15.75 | 1st Qu.:3.0 | Ein Yaakov : 30 | Near:220 | Carmel :150 | 1st Qu.:-0.2713 | 1st Qu.: 0.5702 | 1st Qu.:-0.8215 | |
| Median : 24.00 | Median :5.0 | Givat Yearim : 30 | NA | Galilee :145 | Median : 0.4918 | Median : 0.8140 | Median :-0.5808 | |
| Mean : 30.45 | Mean :4.8 | Givat Yeshayahu: 30 | NA | NA | Mean : 0.3205 | Mean : 0.7098 | Mean :-0.5864 | |
| 3rd Qu.: 36.00 | 3rd Qu.:7.0 | Goren : 30 | NA | NA | 3rd Qu.: 1.1023 | 3rd Qu.: 0.9413 | 3rd Qu.:-0.3375 | |
| Max. :345.00 | Max. :9.0 | Kerem Maharal : 30 | NA | NA | Max. : 1.7127 | Max. : 0.9976 | Max. :-0.0688 | |
| NA | NA | (Other) :263 | NA | NA | NA | NA | NA |
Some outliers with total abundance >100. Examine:
## subunit point_name datetime monitors_name
## 1: Judean Highlands Givat Yeshayahu Far 2 2017-04-20 10:20:00 Eran Banker
## 2: Judean Highlands Givat Yeshayahu Near 1 2017-04-20 06:25:00 Eran Banker
## 3: Judean Highlands Givat Yeshayahu Near 2 2017-04-20 06:50:00 Eran Banker
## 4: Judean Highlands Givat Yeshayahu Near 3 2017-04-20 07:15:00 Eran Banker
## 5: Judean Highlands Aderet Near 2 2019-05-26 06:52:00 Eran Banker
## 6: Carmel Beit Oren Near 1 2019-04-19 07:49:00 Other
## 7: Carmel Beit Oren Near 3 2019-04-19 07:35:00 Other
## 8: Carmel Kerem Maharal Near 3 2021-04-17 07:41:00 Eliraz Dvir
## 9: Carmel Nir Etzion Far 11 2021-04-23 07:24:00 Eliraz Dvir
## richness gma abundance
## 1: 11 5.356635 115
## 2: 13 9.170560 140
## 3: 14 7.652753 138
## 4: 16 9.098580 221
## 5: 15 5.408017 106
## 6: 5 8.043088 129
## 7: 10 7.338970 254
## 8: 11 10.301194 345
## 9: 9 3.066833 119Exclude 3 plots with high abundance (>150) to improve model fit.
PHI>1, hence choose negative binomial. Fit fixed and mixed models. Choose mixed model if possible, otherwise choose a model with fixed-effects only.
## Warning in checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, :
## Model failed to converge with max|grad| = 0.00266732 (tol = 0.002, component 1)mixed model converged. Perform stepwise model selection of mixed model.
## Warning in checkConv(attr(opt, "derivs"), opt$par, ctrl = control$checkConv, :
## Model failed to converge with max|grad| = 0.0044521 (tol = 0.002, component 1)## Single term deletions
##
## Model:
## abundance ~ settlements * year_ct + subunit * year_ct + cos_td_rad +
## sin_td_rad + (1 | site)
## npar AIC
## <none> 3678.7
## cos_td_rad 1 3696.7
## sin_td_rad 1 3699.1
## settlements:year_ct 1 3676.7
## year_ct:subunit 2 3681.6drop settlements X year because \(\Delta AIC<2\)
## Single term deletions
##
## Model:
## abundance ~ settlements + subunit * year_ct + cos_td_rad + sin_td_rad +
## (1 | site)
## npar AIC
## <none> 3676.7
## settlements 1 3772.0
## cos_td_rad 1 3694.8
## sin_td_rad 1 3697.2
## subunit:year_ct 2 3679.7drop year*subunit
## Single term deletions
##
## Model:
## abundance ~ settlements + subunit + year_ct + cos_td_rad + sin_td_rad +
## (1 | site)
## npar AIC
## <none> 3679.7
## settlements 1 3773.3
## subunit 2 3685.2
## year_ct 1 3678.2
## cos_td_rad 1 3695.2
## sin_td_rad 1 3697.6drop year
## Single term deletions
##
## Model:
## abundance ~ settlements + subunit + cos_td_rad + sin_td_rad +
## (1 | site)
## npar AIC
## <none> 3678.2
## settlements 1 3772.0
## subunit 2 3683.8
## cos_td_rad 1 3693.2
## sin_td_rad 1 3697.8subunit, settlement and time of year remain. The final model:
## Generalized linear mixed model fit by maximum likelihood (Laplace
## Approximation) [glmerMod]
## Family: Negative Binomial(3.3101) ( log )
## Formula: abundance ~ settlements + subunit + cos_td_rad + sin_td_rad +
## (1 | site)
## Data: P.anal
##
## AIC BIC logLik deviance df.resid
## 3678.2 3711.0 -1831.1 3662.2 436
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -1.7208 -0.7138 -0.2446 0.3842 9.2005
##
## Random effects:
## Groups Name Variance Std.Dev.
## site (Intercept) 0.01938 0.1392
## Number of obs: 444, groups: site, 16
##
## Fixed effects:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 1.67516 0.32509 5.153 2.57e-07 ***
## settlementsNear 0.54579 0.05556 9.823 < 2e-16 ***
## subunitCarmel 0.16956 0.11089 1.529 0.1262
## subunitGalilee -0.22714 0.11015 -2.062 0.0392 *
## cos_td_rad 1.02590 0.24294 4.223 2.41e-05 ***
## sin_td_rad -1.16744 0.24800 -4.708 2.51e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) sttlmN sbntCr sbntGl cs_td_
## settlmntsNr -0.111
## subunitCrml -0.214 0.020
## subunitGall -0.226 0.033 0.505
## cos_td_rad -0.946 0.019 0.050 0.043
## sin_td_rad 0.938 -0.017 -0.032 -0.062 -0.903## $site
## (Intercept)
## Abirim -0.11137155
## Aderet 0.16235427
## Beit Oren 0.11023799
## Ein Yaakov 0.01625407
## Givat Yearim -0.19886986
## Givat Yeshayahu 0.17665857
## Goren -0.01370126
## Iftach 0.07733150
## Kerem Maharal 0.13673950
## Kfar Shamai 0.00869344
## Margaliot 0.02457356
## Nehusha -0.07214524
## Nir Etzion -0.15864707
## Ofer -0.04190665
## Ramat Raziel -0.06677795
## Yagur -0.04538202
##
## with conditional variances for "site"## $site
Not a great fit, high residuals. center time of year variables, highly correlated with intercept.
## Generalized linear mixed model fit by maximum likelihood (Laplace
## Approximation) [glmerMod]
## Family: Negative Binomial(3.3101) ( log )
## Formula: abundance ~ settlements + subunit + cos_td_rad_c + sin_td_rad_c +
## (1 | site)
## Data: P.anal
##
## AIC BIC logLik deviance df.resid
## 3678.2 3711.0 -1831.1 3662.2 436
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -1.7208 -0.7138 -0.2446 0.3842 9.2005
##
## Random effects:
## Groups Name Variance Std.Dev.
## site (Intercept) 0.01938 0.1392
## Number of obs: 444, groups: site, 16
##
## Fixed effects:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 3.08791 0.08411 36.711 < 2e-16 ***
## settlementsNear 0.54578 0.05556 9.823 < 2e-16 ***
## subunitCarmel 0.16956 0.11088 1.529 0.1262
## subunitGalilee -0.22714 0.11015 -2.062 0.0392 *
## cos_td_rad_c 1.02590 0.24293 4.223 2.41e-05 ***
## sin_td_rad_c -1.16743 0.24798 -4.708 2.51e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) sttlmN sbntCr sbntGl cs_t__
## settlmntsNr -0.358
## subunitCrml -0.669 0.020
## subunitGall -0.678 0.033 0.505
## cos_td_rd_c -0.047 0.019 0.050 0.043
## sin_td_rd_c 0.044 -0.017 -0.032 -0.062 -0.903Interpretation of abundance model:
| Observations | 444 |
| Dependent variable | abundance |
| Type | Mixed effects generalized linear model |
| Family | Negative Binomial(3.3101) |
| Link | log |
| AIC | 3678.232 |
| BIC | 3710.998 |
| Pseudo-R² (fixed effects) | 0.692 |
| Pseudo-R² (total) | 0.804 |
| exp(Est.) | S.E. | z val. | p | |
|---|---|---|---|---|
| (Intercept) | 21.931 | 0.084 | 36.711 | 0.000 |
| settlementsNear | 1.726 | 0.056 | 9.823 | 0.000 |
| subunitCarmel | 1.185 | 0.111 | 1.529 | 0.126 |
| subunitGalilee | 0.797 | 0.110 | -2.062 | 0.039 |
| cos_td_rad_c | 2.790 | 0.243 | 4.223 | 0.000 |
| sin_td_rad_c | 0.311 | 0.248 | -4.708 | 0.000 |
| Group | Parameter | Std. Dev. |
|---|---|---|
| site | (Intercept) | 0.139 |
| Group | # groups | ICC |
|---|---|---|
| site | 16 | 0.052 |
## Confidence intervals for merMod models is an experimental feature. The
## intervals reflect only the variance of the fixed effects, not the random
## effects.
## Confidence intervals for merMod models is an experimental feature. The
## intervals reflect only the variance of the fixed effects, not the random
## effects.
significantly lower abundance in Galilee subunit and far from settlements. No significant temporal trend.
Near plots have on average 15.9211288 more individuals than far plots, which is 72.5960983 percent higher. Galilee plots have on average 6.4825389 less species than Carmel and Judean highland plots, which is 27.0586105 percent lower.
community analysis using package MVabund
## Overlapping points were shifted along the y-axis to make them visible.##
## PIPING TO 2nd MVFACTOR## Only the variables Curruca.melanocephala, Turdus.merula, Streptopelia.decaocto, Passer.domesticus, Pycnonotus.xanthopygos, Columba.livia, Parus.major, Garrulus.glandarius, Cinnyris.osea, Spilopelia.senegalensis, Cecropis.daurica, Chloris.chloris were included in the plot
## (the variables with highest total abundance).
## Overlapping points were shifted along the y-axis to make them visible.##
## PIPING TO 2nd MVFACTOR## Only the variables Curruca.melanocephala, Turdus.merula, Streptopelia.decaocto, Passer.domesticus, Pycnonotus.xanthopygos, Columba.livia, Parus.major, Garrulus.glandarius, Cinnyris.osea, Spilopelia.senegalensis, Cecropis.daurica, Chloris.chloris were included in the plot
## (the variables with highest total abundance).
There are few observations with counts of >60. Examine these:
## point_name datetime SciName monitors_name
## 1: Kerem Maharal Near 3 2021-04-17 07:41:00 Chloris chloris Eliraz Dvir
## 2: Kerem Maharal Near 3 2021-04-17 07:41:00 Garrulus glandarius Eliraz Dvir
## 3: Beit Oren Near 3 2019-04-19 07:35:00 Curruca curruca Other
## 4: Beit Oren Near 1 2019-04-19 07:49:00 Curruca curruca Other
## notes rad_0_20 rad_20_100 rad_100_250 rad_over_250
## 1: 0 80 0 0
## 2: 0 0 150 0
## 3: <NA> 12 30 100 0
## 4: <NA> 14 35 50 0G. glandarius observation seems highly irregular. Remove altogether, might be a mistake. C. curruca observations are prbably due to migration waves. Remove.
start model specification:
## nb po
## 977.4156 1377.6948## [1] "POISSON"
## [1] "NEGATIVE BINOMIAL"
negative binomial model is better than poisson according to residuals and AIC comparison.
## nb po nb1
## 977.4156 1377.6948 966.7131The addition of the explanatory variable ‘site’ is somewhat improving the AIC of the model. Prefer to exclude site, for simplification. stepwise selection of model:
## Single term deletions
##
## Model:
## spp_no_rare ~ settlements * year_ct + subunit * year_ct + cos_td_rad +
## sin_td_rad
## Df AIC
## <none> 23458
## cos_td_rad 24 23515
## sin_td_rad 24 23529
## settlements:year_ct 24 23439
## year_ct:subunit 48 23489drop settlements X year.
## Single term deletions
##
## Model:
## spp_no_rare ~ settlements + subunit * year_ct + cos_td_rad +
## sin_td_rad
## Df AIC
## <none> 23439
## settlements 24 24254
## cos_td_rad 24 23497
## sin_td_rad 24 23513
## subunit:year_ct 48 23481final model includes settlements, year, subunit, subunit X year, sampling time of year.
##
## Test statistics:
## wald value Pr(>wald)
## (Intercept) 12.136 0.001 ***
## settlementsNear 29.207 0.001 ***
## subunitCarmel 10.785 0.001 ***
## subunitGalilee 7.032 0.034 *
## year_ct 6.666 0.025 *
## cos_td_rad 10.598 0.001 ***
## sin_td_rad 11.410 0.001 ***
## subunitCarmel:year_ct 7.600 0.003 **
## subunitGalilee:year_ct 7.879 0.005 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Test statistic: 39.68, p-value: 0.001
## Arguments:
## Test statistics calculated assuming response assumed to be uncorrelated
## P-value calculated using 999 resampling iterations via pit.trap resampling (to account for correlation in testing).## Analysis of Deviance Table
##
## Model: spp_no_rare ~ settlements + subunit * year_ct + cos_td_rad + sin_td_rad
##
## Multivariate test:
## Res.Df Df.diff Dev Pr(>Dev)
## (Intercept) 443
## settlements 442 1 770.4 0.01 **
## subunit 440 2 426.6 0.01 **
## year_ct 439 1 143.4 0.01 **
## cos_td_rad 438 1 46.9 0.03 *
## sin_td_rad 437 1 109.1 0.01 **
## subunit:year_ct 435 2 137.4 0.01 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Univariate Tests:
## Acridotheres.tristis Alectoris.chukar
## Dev Pr(>Dev) Dev Pr(>Dev)
## (Intercept)
## settlements 79.707 0.01 38.366 0.01
## subunit 39.138 0.01 10.607 0.12
## year_ct 29.844 0.01 9.298 0.05
## cos_td_rad 3.002 0.87 2.276 0.94
## sin_td_rad 5.64 0.37 0.596 0.99
## subunit:year_ct 8.217 0.32 2.436 0.96
## Carduelis.carduelis Cecropis.daurica
## Dev Pr(>Dev) Dev Pr(>Dev)
## (Intercept)
## settlements 8.13 0.07 33.414 0.01
## subunit 21.019 0.01 1.066 0.89
## year_ct 6.527 0.25 1.257 0.98
## cos_td_rad 0.389 1.00 0.127 1.00
## sin_td_rad 1.61 0.96 3.044 0.86
## subunit:year_ct 12.307 0.11 0.41 0.98
## Chloris.chloris Cinnyris.osea Columba.livia
## Dev Pr(>Dev) Dev Pr(>Dev) Dev
## (Intercept)
## settlements 30.55 0.01 41.948 0.01 6.276
## subunit 0.613 0.89 17.867 0.01 19.317
## year_ct 5.072 0.44 3.939 0.64 20.916
## cos_td_rad 0.072 1.00 1.651 1.00 0.01
## sin_td_rad 0.112 0.99 2.01 0.95 11.564
## subunit:year_ct 20.167 0.01 12.677 0.11 2.764
## Corvus.cornix Corvus.monedula
## Pr(>Dev) Dev Pr(>Dev) Dev Pr(>Dev)
## (Intercept)
## settlements 0.13 22.932 0.01 0.428 0.57
## subunit 0.01 47.477 0.01 22.714 0.01
## year_ct 0.01 0.695 1.00 0.301 1.00
## cos_td_rad 1.00 1.013 1.00 0.184 1.00
## sin_td_rad 0.04 0.157 0.99 0.053 0.99
## subunit:year_ct 0.96 7.109 0.40 5.316 0.77
## Curruca.curruca Curruca.melanocephala
## Dev Pr(>Dev) Dev Pr(>Dev)
## (Intercept)
## settlements 2.096 0.57 21.24 0.01
## subunit 27.501 0.01 41.067 0.01
## year_ct 13.288 0.02 0.747 1.00
## cos_td_rad 7.65 0.12 0.3 1.00
## sin_td_rad 4.442 0.59 0.429 0.99
## subunit:year_ct 0.001 0.98 9.877 0.16
## Dendrocopos.syriacus Falco.tinnunculus
## Dev Pr(>Dev) Dev Pr(>Dev)
## (Intercept)
## settlements 9.285 0.04 1.849 0.57
## subunit 3.648 0.65 9.122 0.16
## year_ct 0.002 1.00 0.543 1.00
## cos_td_rad 1.417 1.00 0.078 1.00
## sin_td_rad 3.35 0.86 0.641 0.99
## subunit:year_ct 0.232 0.98 5.248 0.77
## Garrulus.glandarius Parus.major
## Dev Pr(>Dev) Dev Pr(>Dev)
## (Intercept)
## settlements 3.502 0.37 3.908 0.37
## subunit 24.625 0.01 25.606 0.01
## year_ct 4.924 0.46 0.176 1.00
## cos_td_rad 1.156 1.00 3.376 0.82
## sin_td_rad 1.081 0.99 7.701 0.16
## subunit:year_ct 5.242 0.77 6.652 0.53
## Passer.domesticus Prinia.gracilis
## Dev Pr(>Dev) Dev Pr(>Dev)
## (Intercept)
## settlements 166.539 0.01 48.787 0.01
## subunit 21.305 0.01 1.864 0.88
## year_ct 1.781 0.91 16.036 0.01
## cos_td_rad 0.485 1.00 0.633 1.00
## sin_td_rad 2.962 0.86 1.004 0.99
## subunit:year_ct 2.283 0.96 13.996 0.05
## Psittacula.krameri Pycnonotus.xanthopygos
## Dev Pr(>Dev) Dev Pr(>Dev)
## (Intercept)
## settlements 15.594 0.01 45.339 0.01
## subunit 14.393 0.04 25.29 0.01
## year_ct 1.082 0.99 2.87 0.81
## cos_td_rad 0.793 1.00 11.394 0.03
## sin_td_rad 1.724 0.96 0.499 0.99
## subunit:year_ct 3.863 0.84 3.75 0.84
## Spilopelia.senegalensis Streptopelia.decaocto
## Dev Pr(>Dev) Dev Pr(>Dev)
## (Intercept)
## settlements 157.013 0.01 1.955 0.57
## subunit 27.046 0.01 12.168 0.04
## year_ct 2.224 0.84 0.068 1.00
## cos_td_rad 0.333 1.00 6.672 0.22
## sin_td_rad 0.603 0.99 14.008 0.01
## subunit:year_ct 4.692 0.77 1.683 0.96
## Streptopelia.turtur Troglodytes.troglodytes
## Dev Pr(>Dev) Dev Pr(>Dev)
## (Intercept)
## settlements 1.175 0.57 26.472 0.01
## subunit 6.566 0.35 4.411 0.55
## year_ct 18.089 0.01 0.576 1.00
## cos_td_rad 3.045 0.87 0.48 1.00
## sin_td_rad 1.847 0.95 10.786 0.07
## subunit:year_ct 1.887 0.96 5.003 0.77
## Turdus.merula
## Dev Pr(>Dev)
## (Intercept)
## settlements 3.926 0.37
## subunit 2.142 0.88
## year_ct 3.137 0.78
## cos_td_rad 0.347 1.00
## sin_td_rad 33.19 0.01
## subunit:year_ct 1.539 0.96
## Arguments:
## Test statistics calculated assuming uncorrelated response (for faster computation)
## P-value calculated using 99 iterations via PIT-trap resampling.Factors settlements, year, subunit, subunit X year, time of year and site have a statistically significant effect on community composition. settlements X year nearly significant.
## Warning: Using `size` aesthetic for lines was deprecated in ggplot2 3.4.0.
## ℹ Please use `linewidth` instead.
## This warning is displayed once every 8 hours.
## Call `lifecycle::last_lifecycle_warnings()` to see where this warning was
## generated.## [[1]]
##
## [[2]]
##
## [[3]]
## [[1]]
##
## [[2]]
##
## [[3]]
Significant negative temporal effect on graceful prinia, European turtle dove and red-rumped swallow; strong positive effect on common myna; positive effect on chukar, greenfinch and pigeon. Significant effect of settlement proximity: most of the synanthrope / invasive species are near settlements.
## (Intercept) settlementsNear subunitCarmel
## -1.639076480 1.570553557 0.648027300
## subunitGalilee year_ct cos_td_rad
## 1.112874781 0.014214819 0.259770952
## sin_td_rad subunitCarmel:year_ct subunitGalilee:year_ct
## 0.004837119 -0.074592027 -0.277566041## (Intercept) settlementsNear year_ct
## 0.00614275 0.93149939 -0.18209987
## subunitCarmel subunitGalilee cos_td_rad
## 0.27673463 -0.09600060 -0.20240622
## sin_td_rad settlementsNear:year_ct
## 0.72573393 0.14416050
## (Intercept) settlementsNear subunitCarmel
## -4.14079167 -0.31938110 1.08645580
## subunitGalilee year_ct cos_td_rad
## 0.08358363 -0.13956880 2.85413650
## sin_td_rad subunitCarmel:year_ct subunitGalilee:year_ct
## -1.72994546 -0.07672922 0.04867093## (Intercept) settlementsNear year_ct
## -4.07155881 -0.27683920 -0.14582746
## subunitCarmel subunitGalilee cos_td_rad
## 0.81205833 0.27579877 2.82345513
## sin_td_rad settlementsNear:year_ct
## -1.68343705 -0.01017195
## (Intercept) settlementsNear subunitCarmel
## -4.66317068 5.01435748 -2.07841381
## subunitGalilee year_ct cos_td_rad
## -0.05133138 -0.19263807 1.33066601
## sin_td_rad subunitCarmel:year_ct subunitGalilee:year_ct
## -2.02686309 0.17563038 0.09562804## (Intercept) settlementsNear year_ct
## -4.93430704 4.64802831 -0.19184173
## subunitCarmel subunitGalilee cos_td_rad
## -1.25853844 0.39004785 1.45064693
## sin_td_rad settlementsNear:year_ct
## -2.30451877 0.08422191
## (Intercept) settlementsNear subunitCarmel
## -5.35172149 3.06499054 -0.51473644
## subunitGalilee year_ct cos_td_rad
## -8.97249477 0.07641756 0.96998632
## sin_td_rad subunitCarmel:year_ct subunitGalilee:year_ct
## -2.74987999 0.08548671 0.82610687## (Intercept) settlementsNear year_ct
## -6.67914086 3.99477207 0.27139139
## subunitCarmel subunitGalilee cos_td_rad
## -0.07163618 -2.84080140 1.05294894
## sin_td_rad settlementsNear:year_ct
## -2.87492784 -0.14351643
