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Table 4 Parameter estimates for the generalised hd models selected (all parameters were significant at p < 0.05; standard errors in brackets)

From: Can random components explain differences in the height–diameter relationship in mixed uneven-aged stands?

Model

Species

Parameter estimates

a 0

a 1

a 2

a 3

a 4

σw0

σw4

σv0

σv1

σv4

σ2

Eq. 10

All

2.164

0.8079

1.478

0.2722

1.035

0.2681

0.006324

0.02413

0

0.03081

5.780

(0.240)

(0.0314)

(0.173)

(0.1225)

(0.030)

(0.0988)

(0.002826)

(0.00385)

(0.00418)

(0.055)

Eq. 12

1

0.7750

1.197

1.538

0.8350

1.641

0.004639

0

0

5.317

(0.3382)

(0.155)

(0.529)

(0.3838)

(0.177)

(0.002198)

(0.379)

2

5.865

0.6090

0.4614

0.6581

0.8085

0.2047

0

0.002967

4.516

(1.900)

(0.0839)

(0.1492)

(0.3003)

(0.0646)

(0.1106)

(0.001716)

(0.212)

3

1.886

0.8951

0.8445

1*

1.042

0.05336

0

0.03282

5.039

(0.476)

(0.0850)

(0.0831)

(0.059)

(0.01402)

(0.00920)

(0.150)

4

2.740

0.7499

0.9867

1*

1.108

0.04699

0

0.04040

5.511

(0.349)

(0.0427)

(0.0518)

(0.039)

(0.010071)

(0.00708)

(0.101)

5

8.185

0.3801

1.181

1*

1.381

0.6424

0

0.06776

6.915

(3.067)

(0.1339)

(0.2812)

(0.248)

(0.3537)

(0.03832)

(0.654)

6

8.139

0.3893

4.147

−1.048

0.8855

0

0

0.3381

5.843

(2.306)

(0.0901)

(1.992)

(0.522)

(0.0969)

(0.0151)

(0.344)

7

3.210

0.7436

0.8383

1*

1.203

0.2229

0

0

4.442

(0.977)

(0.1040)

(0.2214)

(0.1435)

(0.0802)

(0.256)

8

2.875

0.7890

0.6567

1*

1.011

0.04494

0

0.01929

4.490

(0.497)

(0.0570)

(0.0932)

(0.0591)

(0.01718)

(0.00506)

(0.145)

9

2.804

0.7421

1.206

0.7623

1.188

0.05294

0

0.02158

5.329

(0.602)

(0.0705)

(0.279)

(0.2570)

(0.087)

(0.01813)

(.00884)

(0.2236)

10

0.5128

1.203

0.5791

1.548

0.9945

0.007057

0

0.05564

5.624

(0.1351)

(0.090)

(0.1959)

(0.391)

(0.0583)

(0.001453)

(0.01137)

(0.137)

11

0.5844

1.134

0.7255

1.592

1.164

0.008623

0

0.1147

4.868

(0.1790)

(0.105)

(0.2887)

(0.470)

(0.106)

(0.002161)

(0.0303)

(0.169)

12

1.391

0.9641

0.3954

2.617

1.407

0.007239

0

0

8.492

(0.606)

(0.1325)

(0.1212)

(0.4356)

(0.112)

(0.003348)

(0.719)

13

0.6033

1.231

0.2048

2.293

0.9332

0

0

0

8.491

(0.2821)

(0.141)

(0.09188)

(0.536)

(0.0747)

(0.697)

14

1.663

0.8710

0.3988

0.9059

0.7803

0.05772

0

0

3.464

(0.612)

(0.0961)

(0.1881)

(0.4100)

(0.0681)

(0.01480)

(0.161)

15

1*

0.9750

0.7061

1*

1*

0

0.008882

0

3.083

(0.0334)

(0.0797)

(0.002635)

(0.214)

16

1.376

0.7622

0.6975

1*

0.8648

0.3680

0

0.01428

3.153

(0.454)

(0.0996)

(0.2609)

(0.1172)

(0.0145)

(0.00646)

(0.158)

  1. All the variables are as previously defined
  2. *p < 0.05: These parameters were not significant at this level and were fixed at 1 in the final model fitting. This produces slightly different models for each species. A value of 0 for the variance of a random effect indicates that this variance was not significant. A hyphen indicates that this parameter was not part of the model