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Table 2 Jimma Infant Growth Study

From: Modeling overdispersed longitudinal binary data using a combined beta and normal random-effects model

Effect

Parameter

Logistic

Beta-binomial

  

Estimate (s.e.,p)

Estimate (s.e.,p)

Intercept

ξ0

−1.896(0.128, 0.001)

−0.448(1.099, 0.683)

Time

ξ1

0.127(0.031, 0.001)

0.188(0.090, 0.037)

Gender:Male

ξ2

0.027(0.025, 0.294)

0.029(0.039, 0.456)

Place rural

ξ3

−0.602(0.029, 0.001)

−0.949(0.501, 0.058)

Place urban

ξ4

−0.376(0.037, 0.001)

−0.628(0.381, 0.099)

Breast feeding

ξ5

0.545(0.128, 0.001)

0.788(0.347, 0.023)

Slope Gender:Male

ξ6

−0.003(0.006, 0.602)

−0.007(0.011, 0.534)

Slope rural

ξ7

0.018(0.007, 0.014)

0.029(0.020, 0.161)

Slope urban

ξ8

0.016(0.009, 0.097)

0.026(0.022, 0.251)

Slope Breast feeding

ξ9

−0.133(0.031, 0.001)

0.199(0.098, 0.041)

Std. dev. random intercept

d 0

Std. dev. random slope

d 1

Ratio

α/β

1.827(1.622, 0.259)

2log-likelihood

 

41,286

41,286

Effect

Parameter

Logistic-normal

Combined

  

Estimate (s.e., p )

Estimate (s.e., p )

Intercept

ξ0

−2.741(0.186, 0.001)

−2.661(0.215, 0.001)

Time

ξ1

0.132(0.042, 0.002)

0.147(0.049, 0.003)

Gender:Male

ξ2

0.010(0.054, 0.852)

0.020(0.064, 0.751)

Place rural

ξ3

−0.908(0.064, 0.001)

−1.058(0.082, 0.001)

Place urban

ξ4

−0.581(0.082, 0.001)

−0.689(0.099, 0.001)

Breast feeding

ξ5

0.635(0.179, 0.001)

0.764(0.209, 0.001)

Slope Gender:Male

ξ6

−0.003(0.010, 0.728)

−0.005(0.012, 0.660)

Slope rural

ξ7

−0.015(0.011, 0.167)

0.024(0.014, 0.085)

Slope urban

ξ8

−0.011(0.014, 0.432)

0.015(0.017, 0.377)

Slope Breast feeding

ξ9

−0.149(0.044, 0.001)

−0.167(0.049, 0.001)

Std. dev. random intercept

d 0

1.774(0.034, 0.001)

2.107(0.088, 0.001)

Std. dev. random slope

d 1

0.193(0.007, 0.001)

0.237(0.014, 0.001)

Ratio

α/β

0.234(0.045, 0.001)

−2log-likelihood

 

37,000

36,971

  1. Parameter estimates, standard errors, and p-values for the regression coefficients in (1) the logistic model, (2) the beta-binomial model, (3) the logistic-normal model, and (4) the combined model. Estimation was done by maximum likelihood using numerical integration over the normal random effect, if present.