IMLEGIT: Independent Multiple Latent Environmental & Genetic...
In LEGIT: Latent Environmental & Genetic InTeraction (LEGIT) Model
Description
Usage
Arguments
Value
References
Examples
Description
Constructs a generalized linear model (glm) with latent variables using alternating optimization. This is an extension of the LEGIT model to accommodate more than 2 latent variables.
Usage
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Arguments
data
data.frame of the dataset to be used.
latent_var
list of data.frame. The elements of the list are the datasets used to construct each latent variable. For interpretability and proper convergence, not using the same variable in more than one latent variable is highly recommended. It is recommended to set names to the list elements to prevent confusion because otherwise, the latent variables will be named L1, L2, ... (See examples below for more details)
formula
Model formula. The names of latent_var can be used in the formula to represent the latent variables. If names(latent_var) is NULL, then L1, L2, ... can be used in the formula to represent the latent variables. Do not manually code interactions, write them in the formula instead (ex: G*E1*E2 or G:E1:E2).
start_latent_var
Optional list of starting points for each latent variable (The list must have the same length as the number of latent variables and each element of the list must have the same length as the number of variables of the corresponding latent variable).
eps
Threshold for convergence (.01 for quick batch simulations, .0001 for accurate results).
maxiter
Maximum number of iterations.
family
Outcome distribution and link function (Default = gaussian).
ylim
Optional vector containing the known min and max of the outcome variable. Even if your outcome is known to be in [a,b], if you assume a Gaussian distribution, predict() could return values outside this range. This parameter ensures that this never happens. This is not necessary with a distribution that already assumes the proper range (ex: [0,1] with binomial distribution).
print
If FALSE, nothing except warnings will be printed. (Default = TRUE).
Value
Returns an object of the class "IMLEGIT" which is list containing, in the following order: a glm fit of the main model, a list of the glm fits of the latent variables and a list of the true model parameters (AIC, BIC, rank, df.residual, null.deviance) for which the individual model parts (main, genetic, environmental) don't estimate properly.
References
Alexia Jolicoeur-Martineau, Ashley Wazana, Eszter Szekely, Meir Steiner, Alison S. Fleming, James L. Kennedy, Michael J. Meaney, Celia M.T. Greenwood and the MAVAN team. Alternating optimization for GxE modelling with weighted genetic and environmental scores: examples from the MAVAN study (2017). arXiv:1703.08111.
Examples
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train = example_2way(500, 1, seed=777)
fit_best = IMLEGIT(train$data, list(G=train$G, E=train$E), y ~ G*E,
list(train$coef_G, train$coef_E))
fit_default = IMLEGIT(train$data, list(G=train$G, E=train$E), y ~ G*E)
summary(fit_default)
summary(fit_best)
train = example_3way_3latent(500, 1, seed=777)
fit_best = IMLEGIT(train$data, train$latent_var, y ~ G*E*Z,
list(train$coef_G, train$coef_E, train$coef_Z))
fit_default = IMLEGIT(train$data, train$latent_var, y ~ G*E*Z)
summary(fit_default)
summary(fit_best)
Example output
Loading required package: formula.tools
Converged in 9 iterations
Converged in 11 iterations
$fit_main
Call:
stats::glm(formula = formula, family = family, data = data, model = FALSE,
y = FALSE)
Deviance Residuals:
Min 1Q Median 3Q Max
-2.78312 -0.57544 0.01023 0.63266 2.72051
Coefficients: (-7 not defined because of singularities)
Estimate Std. Error t value Pr(>|t|)
(Intercept) -0.98949 0.04421 -22.382 < 2e-16 ***
G 2.07210 0.30017 6.903 1.59e-11 ***
E 3.08836 0.05005 61.706 < 2e-16 ***
G:E 5.26692 0.33619 15.666 < 2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
(Dispersion parameter for gaussian family taken to be 0.9588924)
Null deviance: 4333.5 on 499 degrees of freedom
Residual deviance: 468.9 on 489 degrees of freedom
AIC: 1410.8
Number of Fisher Scoring iterations: 2
$fit_G
Call:
stats::glm(formula = formula_step[[i]], family = family, data = data,
model = FALSE, y = FALSE)
Deviance Residuals:
Min 1Q Median 3Q Max
-2.78303 -0.57544 0.01055 0.63263 2.72214
Coefficients: (-5 not defined because of singularities)
Estimate Std. Error t value Pr(>|t|)
g1 0.09097 0.02211 4.114 4.57e-05 ***
g2 0.06109 0.02739 2.230 0.0262 *
g3 -0.30112 0.02053 -14.667 < 2e-16 ***
g4 0.10666 0.02193 4.863 1.56e-06 ***
g1_g3 0.18372 0.04182 4.393 1.37e-05 ***
g2_g3 0.25644 0.04550 5.636 2.94e-08 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
(Dispersion parameter for gaussian family taken to be 0.9588907)
Null deviance: 4333.5 on 500 degrees of freedom
Residual deviance: 468.9 on 489 degrees of freedom
AIC: 1410.8
Number of Fisher Scoring iterations: 2
$fit_E
Call:
stats::glm(formula = formula_step[[i]], family = family, data = data,
model = FALSE, y = FALSE)
Deviance Residuals:
Min 1Q Median 3Q Max
-2.78317 -0.57543 0.01023 0.63265 2.72052
Coefficients: (-8 not defined because of singularities)
Estimate Std. Error t value Pr(>|t|)
e1 -0.458840 0.009451 -48.55 <2e-16 ***
e2 0.349199 0.009151 38.16 <2e-16 ***
e3 0.191962 0.009278 20.69 <2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
(Dispersion parameter for gaussian family taken to be 0.9588924)
Null deviance: 4333.5 on 500 degrees of freedom
Residual deviance: 468.9 on 489 degrees of freedom
AIC: 1410.8
Number of Fisher Scoring iterations: 2
$fit_main
Call:
stats::glm(formula = formula, family = family, data = data, model = FALSE,
y = FALSE)
Deviance Residuals:
Min 1Q Median 3Q Max
-2.78303 -0.57577 0.01051 0.63213 2.72088
Coefficients: (-7 not defined because of singularities)
Estimate Std. Error t value Pr(>|t|)
(Intercept) -0.98932 0.04421 -22.379 < 2e-16 ***
G 2.07182 0.30020 6.901 1.6e-11 ***
E 3.08877 0.05005 61.714 < 2e-16 ***
G:E 5.26743 0.33622 15.667 < 2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
(Dispersion parameter for gaussian family taken to be 0.9588912)
Null deviance: 4333.5 on 499 degrees of freedom
Residual deviance: 468.9 on 489 degrees of freedom
AIC: 1410.8
Number of Fisher Scoring iterations: 2
$fit_G
Call:
stats::glm(formula = formula_step[[i]], family = family, data = data,
model = FALSE, y = FALSE)
Deviance Residuals:
Min 1Q Median 3Q Max
-2.78296 -0.57577 0.01054 0.63210 2.72229
Coefficients: (-5 not defined because of singularities)
Estimate Std. Error t value Pr(>|t|)
g1 0.09090 0.02211 4.111 4.62e-05 ***
g2 0.06104 0.02739 2.228 0.0263 *
g3 -0.30118 0.02053 -14.671 < 2e-16 ***
g4 0.10661 0.02193 4.861 1.58e-06 ***
g1_g3 0.18379 0.04182 4.395 1.36e-05 ***
g2_g3 0.25649 0.04550 5.637 2.92e-08 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
(Dispersion parameter for gaussian family taken to be 0.9588899)
Null deviance: 4333.5 on 500 degrees of freedom
Residual deviance: 468.9 on 489 degrees of freedom
AIC: 1410.8
Number of Fisher Scoring iterations: 2
$fit_E
Call:
stats::glm(formula = formula_step[[i]], family = family, data = data,
model = FALSE, y = FALSE)
Deviance Residuals:
Min 1Q Median 3Q Max
-2.78307 -0.57577 0.01051 0.63212 2.72089
Coefficients: (-8 not defined because of singularities)
Estimate Std. Error t value Pr(>|t|)
e1 -0.458845 0.009452 -48.55 <2e-16 ***
e2 0.349195 0.009151 38.16 <2e-16 ***
e3 0.191961 0.009278 20.69 <2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
(Dispersion parameter for gaussian family taken to be 0.9588912)
Null deviance: 4333.5 on 500 degrees of freedom
Residual deviance: 468.9 on 489 degrees of freedom
AIC: 1410.8
Number of Fisher Scoring iterations: 2
Converged in 6 iterations
Converged in 8 iterations
$fit_main
Call:
stats::glm(formula = formula, family = family, data = data, model = FALSE,
y = FALSE)
Deviance Residuals:
Min 1Q Median 3Q Max
-3.2859 -0.6868 0.0383 0.6744 3.0719
Coefficients: (-9 not defined because of singularities)
Estimate Std. Error t value Pr(>|t|)
(Intercept) -2.18841 0.20357 -10.750 < 2e-16 ***
G 3.58237 1.10101 3.254 0.00122 **
E 2.91802 0.24181 12.067 < 2e-16 ***
Z 1.02907 0.06514 15.797 < 2e-16 ***
G:E 7.54922 1.44259 5.233 2.49e-07 ***
G:Z 1.61548 0.34724 4.652 4.24e-06 ***
E:Z -1.53780 0.07488 -20.537 < 2e-16 ***
G:E:Z 1.41976 0.43812 3.241 0.00128 **
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
(Dispersion parameter for gaussian family taken to be 1.095196)
Null deviance: 5134.92 on 499 degrees of freedom
Residual deviance: 528.98 on 483 degrees of freedom
AIC: 1483.1
Number of Fisher Scoring iterations: 2
$fit_G
Call:
stats::glm(formula = formula_step[[i]], family = family, data = data,
model = FALSE, y = FALSE)
Deviance Residuals:
Min 1Q Median 3Q Max
-3.2859 -0.6850 0.0383 0.6748 3.0726
Coefficients: (-11 not defined because of singularities)
Estimate Std. Error t value Pr(>|t|)
g1 0.196216 0.009334 21.021 < 2e-16 ***
g2 0.163200 0.010855 15.035 < 2e-16 ***
g3 -0.289568 0.008224 -35.211 < 2e-16 ***
g4 0.114555 0.008830 12.974 < 2e-16 ***
g1_g3 0.058679 0.016888 3.475 0.000558 ***
g2_g3 0.177782 0.018256 9.738 < 2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
(Dispersion parameter for gaussian family taken to be 1.095187)
Null deviance: 5134.92 on 500 degrees of freedom
Residual deviance: 528.98 on 483 degrees of freedom
AIC: 1483.1
Number of Fisher Scoring iterations: 2
$fit_E
Call:
stats::glm(formula = formula_step[[i]], family = family, data = data,
model = FALSE, y = FALSE)
Deviance Residuals:
Min 1Q Median 3Q Max
-3.2858 -0.6869 0.0383 0.6744 3.0725
Coefficients: (-14 not defined because of singularities)
Estimate Std. Error t value Pr(>|t|)
e1 -0.44290 0.01185 -37.36 <2e-16 ***
e2 0.33701 0.01285 26.24 <2e-16 ***
e3 0.22008 0.01279 17.21 <2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
(Dispersion parameter for gaussian family taken to be 1.095196)
Null deviance: 5134.92 on 500 degrees of freedom
Residual deviance: 528.98 on 483 degrees of freedom
AIC: 1483.1
Number of Fisher Scoring iterations: 2
$fit_Z
Call:
stats::glm(formula = formula_step[[i]], family = family, data = data,
model = FALSE, y = FALSE)
Deviance Residuals:
Min 1Q Median 3Q Max
-3.2861 -0.6868 0.0385 0.6743 3.0723
Coefficients: (-14 not defined because of singularities)
Estimate Std. Error t value Pr(>|t|)
z1 0.18158 0.02052 8.849 < 2e-16 ***
z2 0.74541 0.02135 34.921 < 2e-16 ***
z3 0.07302 0.01985 3.679 0.00026 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
(Dispersion parameter for gaussian family taken to be 1.095196)
Null deviance: 5134.92 on 500 degrees of freedom
Residual deviance: 528.98 on 483 degrees of freedom
AIC: 1483.1
Number of Fisher Scoring iterations: 2
$fit_main
Call:
stats::glm(formula = formula, family = family, data = data, model = FALSE,
y = FALSE)
Deviance Residuals:
Min 1Q Median 3Q Max
-3.2843 -0.6890 0.0256 0.6746 3.0711
Coefficients: (-9 not defined because of singularities)
Estimate Std. Error t value Pr(>|t|)
(Intercept) -2.18181 0.20304 -10.746 < 2e-16 ***
G 3.60279 1.10178 3.270 0.00115 **
E 2.92403 0.24123 12.122 < 2e-16 ***
Z 1.02969 0.06497 15.849 < 2e-16 ***
G:E 7.52947 1.44405 5.214 2.74e-07 ***
G:Z 1.61119 0.34747 4.637 4.56e-06 ***
E:Z -1.53617 0.07468 -20.570 < 2e-16 ***
G:E:Z 1.42947 0.43858 3.259 0.00120 **
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
(Dispersion parameter for gaussian family taken to be 1.095191)
Null deviance: 5134.92 on 499 degrees of freedom
Residual deviance: 528.98 on 483 degrees of freedom
AIC: 1483.1
Number of Fisher Scoring iterations: 2
$fit_G
Call:
stats::glm(formula = formula_step[[i]], family = family, data = data,
model = FALSE, y = FALSE)
Deviance Residuals:
Min 1Q Median 3Q Max
-3.2843 -0.6911 0.0256 0.6693 3.0705
Coefficients: (-11 not defined because of singularities)
Estimate Std. Error t value Pr(>|t|)
g1 0.195433 0.009330 20.946 < 2e-16 ***
g2 0.162524 0.010851 14.977 < 2e-16 ***
g3 -0.290351 0.008221 -35.317 < 2e-16 ***
g4 0.113960 0.008828 12.909 < 2e-16 ***
g1_g3 0.059325 0.016885 3.514 0.000484 ***
g2_g3 0.178407 0.018251 9.775 < 2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
(Dispersion parameter for gaussian family taken to be 1.095183)
Null deviance: 5134.92 on 500 degrees of freedom
Residual deviance: 528.97 on 483 degrees of freedom
AIC: 1483.1
Number of Fisher Scoring iterations: 2
$fit_E
Call:
stats::glm(formula = formula_step[[i]], family = family, data = data,
model = FALSE, y = FALSE)
Deviance Residuals:
Min 1Q Median 3Q Max
-3.2844 -0.6890 0.0256 0.6746 3.0706
Coefficients: (-14 not defined because of singularities)
Estimate Std. Error t value Pr(>|t|)
e1 -0.44272 0.01185 -37.36 <2e-16 ***
e2 0.33728 0.01285 26.25 <2e-16 ***
e3 0.21999 0.01278 17.21 <2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
(Dispersion parameter for gaussian family taken to be 1.095191)
Null deviance: 5134.92 on 500 degrees of freedom
Residual deviance: 528.98 on 483 degrees of freedom
AIC: 1483.1
Number of Fisher Scoring iterations: 2
$fit_Z
Call:
stats::glm(formula = formula_step[[i]], family = family, data = data,
model = FALSE, y = FALSE)
Deviance Residuals:
Min 1Q Median 3Q Max
-3.2841 -0.6890 0.0254 0.6747 3.0708
Coefficients: (-14 not defined because of singularities)
Estimate Std. Error t value Pr(>|t|)
z1 0.18131 0.02054 8.830 < 2e-16 ***
z2 0.74581 0.02136 34.913 < 2e-16 ***
z3 0.07287 0.01986 3.669 0.00027 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
(Dispersion parameter for gaussian family taken to be 1.09519)
Null deviance: 5134.92 on 500 degrees of freedom
Residual deviance: 528.98 on 483 degrees of freedom
AIC: 1483.1
Number of Fisher Scoring iterations: 2
LEGIT documentation built on Jan. 12, 2022, 1:08 a.m.
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Description Usage Arguments Value References Examples
Description
Constructs a generalized linear model (glm) with latent variables using alternating optimization. This is an extension of the LEGIT model to accommodate more than 2 latent variables.
Usage
1 2 3 4 5 6 7 8 9 10 11 |
Arguments
data |
data.frame of the dataset to be used. |
latent_var |
list of data.frame. The elements of the list are the datasets used to construct each latent variable. For interpretability and proper convergence, not using the same variable in more than one latent variable is highly recommended. It is recommended to set names to the list elements to prevent confusion because otherwise, the latent variables will be named L1, L2, ... (See examples below for more details) |
formula |
Model formula. The names of |
start_latent_var |
Optional list of starting points for each latent variable (The list must have the same length as the number of latent variables and each element of the list must have the same length as the number of variables of the corresponding latent variable). |
eps |
Threshold for convergence (.01 for quick batch simulations, .0001 for accurate results). |
maxiter |
Maximum number of iterations. |
family |
Outcome distribution and link function (Default = gaussian). |
ylim |
Optional vector containing the known min and max of the outcome variable. Even if your outcome is known to be in [a,b], if you assume a Gaussian distribution, predict() could return values outside this range. This parameter ensures that this never happens. This is not necessary with a distribution that already assumes the proper range (ex: [0,1] with binomial distribution). |
print |
If FALSE, nothing except warnings will be printed. (Default = TRUE). |
Value
Returns an object of the class "IMLEGIT" which is list containing, in the following order: a glm fit of the main model, a list of the glm fits of the latent variables and a list of the true model parameters (AIC, BIC, rank, df.residual, null.deviance) for which the individual model parts (main, genetic, environmental) don't estimate properly.
References
Alexia Jolicoeur-Martineau, Ashley Wazana, Eszter Szekely, Meir Steiner, Alison S. Fleming, James L. Kennedy, Michael J. Meaney, Celia M.T. Greenwood and the MAVAN team. Alternating optimization for GxE modelling with weighted genetic and environmental scores: examples from the MAVAN study (2017). arXiv:1703.08111.
Examples
1 2 3 4 5 6 7 8 9 10 11 12 | train = example_2way(500, 1, seed=777)
fit_best = IMLEGIT(train$data, list(G=train$G, E=train$E), y ~ G*E,
list(train$coef_G, train$coef_E))
fit_default = IMLEGIT(train$data, list(G=train$G, E=train$E), y ~ G*E)
summary(fit_default)
summary(fit_best)
train = example_3way_3latent(500, 1, seed=777)
fit_best = IMLEGIT(train$data, train$latent_var, y ~ G*E*Z,
list(train$coef_G, train$coef_E, train$coef_Z))
fit_default = IMLEGIT(train$data, train$latent_var, y ~ G*E*Z)
summary(fit_default)
summary(fit_best)
|
Example output
Loading required package: formula.tools
Converged in 9 iterations
Converged in 11 iterations
$fit_main
Call:
stats::glm(formula = formula, family = family, data = data, model = FALSE,
y = FALSE)
Deviance Residuals:
Min 1Q Median 3Q Max
-2.78312 -0.57544 0.01023 0.63266 2.72051
Coefficients: (-7 not defined because of singularities)
Estimate Std. Error t value Pr(>|t|)
(Intercept) -0.98949 0.04421 -22.382 < 2e-16 ***
G 2.07210 0.30017 6.903 1.59e-11 ***
E 3.08836 0.05005 61.706 < 2e-16 ***
G:E 5.26692 0.33619 15.666 < 2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
(Dispersion parameter for gaussian family taken to be 0.9588924)
Null deviance: 4333.5 on 499 degrees of freedom
Residual deviance: 468.9 on 489 degrees of freedom
AIC: 1410.8
Number of Fisher Scoring iterations: 2
$fit_G
Call:
stats::glm(formula = formula_step[[i]], family = family, data = data,
model = FALSE, y = FALSE)
Deviance Residuals:
Min 1Q Median 3Q Max
-2.78303 -0.57544 0.01055 0.63263 2.72214
Coefficients: (-5 not defined because of singularities)
Estimate Std. Error t value Pr(>|t|)
g1 0.09097 0.02211 4.114 4.57e-05 ***
g2 0.06109 0.02739 2.230 0.0262 *
g3 -0.30112 0.02053 -14.667 < 2e-16 ***
g4 0.10666 0.02193 4.863 1.56e-06 ***
g1_g3 0.18372 0.04182 4.393 1.37e-05 ***
g2_g3 0.25644 0.04550 5.636 2.94e-08 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
(Dispersion parameter for gaussian family taken to be 0.9588907)
Null deviance: 4333.5 on 500 degrees of freedom
Residual deviance: 468.9 on 489 degrees of freedom
AIC: 1410.8
Number of Fisher Scoring iterations: 2
$fit_E
Call:
stats::glm(formula = formula_step[[i]], family = family, data = data,
model = FALSE, y = FALSE)
Deviance Residuals:
Min 1Q Median 3Q Max
-2.78317 -0.57543 0.01023 0.63265 2.72052
Coefficients: (-8 not defined because of singularities)
Estimate Std. Error t value Pr(>|t|)
e1 -0.458840 0.009451 -48.55 <2e-16 ***
e2 0.349199 0.009151 38.16 <2e-16 ***
e3 0.191962 0.009278 20.69 <2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
(Dispersion parameter for gaussian family taken to be 0.9588924)
Null deviance: 4333.5 on 500 degrees of freedom
Residual deviance: 468.9 on 489 degrees of freedom
AIC: 1410.8
Number of Fisher Scoring iterations: 2
$fit_main
Call:
stats::glm(formula = formula, family = family, data = data, model = FALSE,
y = FALSE)
Deviance Residuals:
Min 1Q Median 3Q Max
-2.78303 -0.57577 0.01051 0.63213 2.72088
Coefficients: (-7 not defined because of singularities)
Estimate Std. Error t value Pr(>|t|)
(Intercept) -0.98932 0.04421 -22.379 < 2e-16 ***
G 2.07182 0.30020 6.901 1.6e-11 ***
E 3.08877 0.05005 61.714 < 2e-16 ***
G:E 5.26743 0.33622 15.667 < 2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
(Dispersion parameter for gaussian family taken to be 0.9588912)
Null deviance: 4333.5 on 499 degrees of freedom
Residual deviance: 468.9 on 489 degrees of freedom
AIC: 1410.8
Number of Fisher Scoring iterations: 2
$fit_G
Call:
stats::glm(formula = formula_step[[i]], family = family, data = data,
model = FALSE, y = FALSE)
Deviance Residuals:
Min 1Q Median 3Q Max
-2.78296 -0.57577 0.01054 0.63210 2.72229
Coefficients: (-5 not defined because of singularities)
Estimate Std. Error t value Pr(>|t|)
g1 0.09090 0.02211 4.111 4.62e-05 ***
g2 0.06104 0.02739 2.228 0.0263 *
g3 -0.30118 0.02053 -14.671 < 2e-16 ***
g4 0.10661 0.02193 4.861 1.58e-06 ***
g1_g3 0.18379 0.04182 4.395 1.36e-05 ***
g2_g3 0.25649 0.04550 5.637 2.92e-08 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
(Dispersion parameter for gaussian family taken to be 0.9588899)
Null deviance: 4333.5 on 500 degrees of freedom
Residual deviance: 468.9 on 489 degrees of freedom
AIC: 1410.8
Number of Fisher Scoring iterations: 2
$fit_E
Call:
stats::glm(formula = formula_step[[i]], family = family, data = data,
model = FALSE, y = FALSE)
Deviance Residuals:
Min 1Q Median 3Q Max
-2.78307 -0.57577 0.01051 0.63212 2.72089
Coefficients: (-8 not defined because of singularities)
Estimate Std. Error t value Pr(>|t|)
e1 -0.458845 0.009452 -48.55 <2e-16 ***
e2 0.349195 0.009151 38.16 <2e-16 ***
e3 0.191961 0.009278 20.69 <2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
(Dispersion parameter for gaussian family taken to be 0.9588912)
Null deviance: 4333.5 on 500 degrees of freedom
Residual deviance: 468.9 on 489 degrees of freedom
AIC: 1410.8
Number of Fisher Scoring iterations: 2
Converged in 6 iterations
Converged in 8 iterations
$fit_main
Call:
stats::glm(formula = formula, family = family, data = data, model = FALSE,
y = FALSE)
Deviance Residuals:
Min 1Q Median 3Q Max
-3.2859 -0.6868 0.0383 0.6744 3.0719
Coefficients: (-9 not defined because of singularities)
Estimate Std. Error t value Pr(>|t|)
(Intercept) -2.18841 0.20357 -10.750 < 2e-16 ***
G 3.58237 1.10101 3.254 0.00122 **
E 2.91802 0.24181 12.067 < 2e-16 ***
Z 1.02907 0.06514 15.797 < 2e-16 ***
G:E 7.54922 1.44259 5.233 2.49e-07 ***
G:Z 1.61548 0.34724 4.652 4.24e-06 ***
E:Z -1.53780 0.07488 -20.537 < 2e-16 ***
G:E:Z 1.41976 0.43812 3.241 0.00128 **
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
(Dispersion parameter for gaussian family taken to be 1.095196)
Null deviance: 5134.92 on 499 degrees of freedom
Residual deviance: 528.98 on 483 degrees of freedom
AIC: 1483.1
Number of Fisher Scoring iterations: 2
$fit_G
Call:
stats::glm(formula = formula_step[[i]], family = family, data = data,
model = FALSE, y = FALSE)
Deviance Residuals:
Min 1Q Median 3Q Max
-3.2859 -0.6850 0.0383 0.6748 3.0726
Coefficients: (-11 not defined because of singularities)
Estimate Std. Error t value Pr(>|t|)
g1 0.196216 0.009334 21.021 < 2e-16 ***
g2 0.163200 0.010855 15.035 < 2e-16 ***
g3 -0.289568 0.008224 -35.211 < 2e-16 ***
g4 0.114555 0.008830 12.974 < 2e-16 ***
g1_g3 0.058679 0.016888 3.475 0.000558 ***
g2_g3 0.177782 0.018256 9.738 < 2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
(Dispersion parameter for gaussian family taken to be 1.095187)
Null deviance: 5134.92 on 500 degrees of freedom
Residual deviance: 528.98 on 483 degrees of freedom
AIC: 1483.1
Number of Fisher Scoring iterations: 2
$fit_E
Call:
stats::glm(formula = formula_step[[i]], family = family, data = data,
model = FALSE, y = FALSE)
Deviance Residuals:
Min 1Q Median 3Q Max
-3.2858 -0.6869 0.0383 0.6744 3.0725
Coefficients: (-14 not defined because of singularities)
Estimate Std. Error t value Pr(>|t|)
e1 -0.44290 0.01185 -37.36 <2e-16 ***
e2 0.33701 0.01285 26.24 <2e-16 ***
e3 0.22008 0.01279 17.21 <2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
(Dispersion parameter for gaussian family taken to be 1.095196)
Null deviance: 5134.92 on 500 degrees of freedom
Residual deviance: 528.98 on 483 degrees of freedom
AIC: 1483.1
Number of Fisher Scoring iterations: 2
$fit_Z
Call:
stats::glm(formula = formula_step[[i]], family = family, data = data,
model = FALSE, y = FALSE)
Deviance Residuals:
Min 1Q Median 3Q Max
-3.2861 -0.6868 0.0385 0.6743 3.0723
Coefficients: (-14 not defined because of singularities)
Estimate Std. Error t value Pr(>|t|)
z1 0.18158 0.02052 8.849 < 2e-16 ***
z2 0.74541 0.02135 34.921 < 2e-16 ***
z3 0.07302 0.01985 3.679 0.00026 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
(Dispersion parameter for gaussian family taken to be 1.095196)
Null deviance: 5134.92 on 500 degrees of freedom
Residual deviance: 528.98 on 483 degrees of freedom
AIC: 1483.1
Number of Fisher Scoring iterations: 2
$fit_main
Call:
stats::glm(formula = formula, family = family, data = data, model = FALSE,
y = FALSE)
Deviance Residuals:
Min 1Q Median 3Q Max
-3.2843 -0.6890 0.0256 0.6746 3.0711
Coefficients: (-9 not defined because of singularities)
Estimate Std. Error t value Pr(>|t|)
(Intercept) -2.18181 0.20304 -10.746 < 2e-16 ***
G 3.60279 1.10178 3.270 0.00115 **
E 2.92403 0.24123 12.122 < 2e-16 ***
Z 1.02969 0.06497 15.849 < 2e-16 ***
G:E 7.52947 1.44405 5.214 2.74e-07 ***
G:Z 1.61119 0.34747 4.637 4.56e-06 ***
E:Z -1.53617 0.07468 -20.570 < 2e-16 ***
G:E:Z 1.42947 0.43858 3.259 0.00120 **
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
(Dispersion parameter for gaussian family taken to be 1.095191)
Null deviance: 5134.92 on 499 degrees of freedom
Residual deviance: 528.98 on 483 degrees of freedom
AIC: 1483.1
Number of Fisher Scoring iterations: 2
$fit_G
Call:
stats::glm(formula = formula_step[[i]], family = family, data = data,
model = FALSE, y = FALSE)
Deviance Residuals:
Min 1Q Median 3Q Max
-3.2843 -0.6911 0.0256 0.6693 3.0705
Coefficients: (-11 not defined because of singularities)
Estimate Std. Error t value Pr(>|t|)
g1 0.195433 0.009330 20.946 < 2e-16 ***
g2 0.162524 0.010851 14.977 < 2e-16 ***
g3 -0.290351 0.008221 -35.317 < 2e-16 ***
g4 0.113960 0.008828 12.909 < 2e-16 ***
g1_g3 0.059325 0.016885 3.514 0.000484 ***
g2_g3 0.178407 0.018251 9.775 < 2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
(Dispersion parameter for gaussian family taken to be 1.095183)
Null deviance: 5134.92 on 500 degrees of freedom
Residual deviance: 528.97 on 483 degrees of freedom
AIC: 1483.1
Number of Fisher Scoring iterations: 2
$fit_E
Call:
stats::glm(formula = formula_step[[i]], family = family, data = data,
model = FALSE, y = FALSE)
Deviance Residuals:
Min 1Q Median 3Q Max
-3.2844 -0.6890 0.0256 0.6746 3.0706
Coefficients: (-14 not defined because of singularities)
Estimate Std. Error t value Pr(>|t|)
e1 -0.44272 0.01185 -37.36 <2e-16 ***
e2 0.33728 0.01285 26.25 <2e-16 ***
e3 0.21999 0.01278 17.21 <2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
(Dispersion parameter for gaussian family taken to be 1.095191)
Null deviance: 5134.92 on 500 degrees of freedom
Residual deviance: 528.98 on 483 degrees of freedom
AIC: 1483.1
Number of Fisher Scoring iterations: 2
$fit_Z
Call:
stats::glm(formula = formula_step[[i]], family = family, data = data,
model = FALSE, y = FALSE)
Deviance Residuals:
Min 1Q Median 3Q Max
-3.2841 -0.6890 0.0254 0.6747 3.0708
Coefficients: (-14 not defined because of singularities)
Estimate Std. Error t value Pr(>|t|)
z1 0.18131 0.02054 8.830 < 2e-16 ***
z2 0.74581 0.02136 34.913 < 2e-16 ***
z3 0.07287 0.01986 3.669 0.00027 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
(Dispersion parameter for gaussian family taken to be 1.09519)
Null deviance: 5134.92 on 500 degrees of freedom
Residual deviance: 528.98 on 483 degrees of freedom
AIC: 1483.1
Number of Fisher Scoring iterations: 2
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