SEM updated
Lisa Merrill
2024-08-19
Loading libraries
library(tidyverse)## ── Attaching core tidyverse packages ──────────────────────── tidyverse 2.0.0 ──
## ✔ dplyr 1.1.3 ✔ readr 2.1.4
## ✔ forcats 1.0.0 ✔ stringr 1.5.1
## ✔ ggplot2 3.4.4 ✔ tibble 3.2.1
## ✔ lubridate 1.9.3 ✔ tidyr 1.3.0
## ✔ purrr 1.0.2
## ── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
## ✖ dplyr::filter() masks stats::filter()
## ✖ dplyr::lag() masks stats::lag()
## ℹ Use the conflicted package (<http://conflicted.r-lib.org/>) to force all conflicts to become errorslibrary(lavaan)## This is lavaan 0.6-18
## lavaan is FREE software! Please report any bugs.#install.packages("semPlot")
library(semPlot)Loading data
db <- read.csv("dairymean_bone.csv")
db2 <-read.csv("dairy_TBS_BMD_cov.csv")#look at variance of inflammation biomarkers
#lapply(db,function(x)var(x,na.rm=T))#variance of each is high; log transform
db$log_crp <- log(db$CRP)
db$log_tnf <-log(db$TNFa)
db$log_IL6 <-log(db$IL6)
db$log_il1B <-log(db$IL1B)
db$log_skim <-log(db$skim)
db2 <-read.csv("dairy_TBS_BMD_cov.csv")
db2$log_crp <-log(db2$CRP)
db2$log_tnf <-log(db2$TNFa)
db2$log_IL6 <-log(db2$IL6)
db2$log_il1B <-log(db2$IL1B)
db2$log_skim <-log(db2$skim + 0.01)Eliminate bone columns 3a, 5a, 5c, 5f because of high NA content
db$bone3a_b2 <- NULL
db$bone5a_b2 <- NULL
db$bone5c_b2 <- NULL
db$bone5f_b2 <- NULL
db2$bone3a_b2 <- NULL
db2$bone5a_b2 <- NULL
db2$bone5c_b2 <- NULL
db2$bone5f_b2 <- NULLEliminate dichotomized variables
# db <- db %>% dplyr::select(!contains("dichot"))
# db2 <- db2 %>% dplyr::select(!contains("dichot"))SEM milk as predictor var, BMSi as response, and IL6, TNFa, IL1B as individual mediators
model_milk <- ' # direct effect
BMSi ~ i*milk
# mediator
IL6 ~ a*milk
TNFa ~ c*milk
IL1B ~ e*milk
CRP ~ g*milk
BMSi ~ b*IL6
BMSi ~ d*TNFa
BMSi ~ f*IL1B
BMSi~ h*CRP
# indirect effect (a*b)
ab := a*b
cd := c*d
ef := e*f
gh :=g*h
# total effect
total := i + (a*b) +(c*d) +(e*f) +(g*h)
'
fit <- sem(model_milk, data = db)
summary(fit)## lavaan 0.6-18 ended normally after 1 iteration
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 14
##
## Used Total
## Number of observations 151 163
##
## Model Test User Model:
##
## Test statistic 8.559
## Degrees of freedom 6
## P-value (Chi-square) 0.200
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Regressions:
## Estimate Std.Err z-value P(>|z|)
## BMSi ~
## milk (i) 0.958 0.852 1.125 0.261
## IL6 ~
## milk (a) -0.588 0.474 -1.241 0.215
## TNFa ~
## milk (c) 0.682 0.743 0.919 0.358
## IL1B ~
## milk (e) -1.824 2.794 -0.653 0.514
## CRP ~
## milk (g) -1.618 0.658 -2.458 0.014
## BMSi ~
## IL6 (b) -0.120 0.142 -0.847 0.397
## TNFa (d) -0.029 0.091 -0.319 0.750
## IL1B (f) -0.019 0.024 -0.768 0.442
## CRP (h) -0.079 0.102 -0.774 0.439
##
## Variances:
## Estimate Std.Err z-value P(>|z|)
## .BMSi 64.811 7.459 8.689 0.000
## .IL6 21.222 2.442 8.689 0.000
## .TNFa 52.186 6.006 8.689 0.000
## .IL1B 738.733 85.019 8.689 0.000
## .CRP 40.972 4.715 8.689 0.000
##
## Defined Parameters:
## Estimate Std.Err z-value P(>|z|)
## ab 0.071 0.101 0.699 0.484
## cd -0.020 0.066 -0.301 0.763
## ef 0.034 0.068 0.497 0.619
## gh 0.128 0.174 0.739 0.460
## total 1.171 0.833 1.405 0.160semPaths(fit)
Fluid dairy
model_fluid <- ' # direct effect
BMSi ~ i*fluid
# mediator
IL6 ~ a*fluid
TNFa ~ c*fluid
IL1B ~ e*fluid
CRP ~ g*fluid
BMSi ~ b*IL6
BMSi ~ d*TNFa
BMSi ~ f*IL1B
BMSi~ h*CRP
# indirect effect (a*b)
ab := a*b
cd := c*d
ef := e*f
gh :=g*h
# total effect
total := i + (a*b) +(c*d) +(e*f) +(g*h)
'
fit <- sem(model_fluid, data = db)
summary(fit)## lavaan 0.6-18 ended normally after 1 iteration
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 14
##
## Used Total
## Number of observations 151 163
##
## Model Test User Model:
##
## Test statistic 8.524
## Degrees of freedom 6
## P-value (Chi-square) 0.202
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Regressions:
## Estimate Std.Err z-value P(>|z|)
## BMSi ~
## fluid (i) 0.871 0.800 1.089 0.276
## IL6 ~
## fluid (a) -0.509 0.446 -1.142 0.253
## TNFa ~
## fluid (c) 0.655 0.698 0.938 0.348
## IL1B ~
## fluid (e) -1.745 2.628 -0.664 0.507
## CRP ~
## fluid (g) -1.470 0.620 -2.371 0.018
## BMSi ~
## IL6 (b) -0.122 0.142 -0.860 0.390
## TNFa (d) -0.029 0.091 -0.316 0.752
## IL1B (f) -0.019 0.024 -0.770 0.442
## CRP (h) -0.081 0.102 -0.790 0.430
##
## Variances:
## Estimate Std.Err z-value P(>|z|)
## .BMSi 64.845 7.463 8.689 0.000
## .IL6 21.255 2.446 8.689 0.000
## .TNFa 52.173 6.004 8.689 0.000
## .IL1B 738.660 85.010 8.689 0.000
## .CRP 41.082 4.728 8.689 0.000
##
## Defined Parameters:
## Estimate Std.Err z-value P(>|z|)
## ab 0.062 0.091 0.687 0.492
## cd -0.019 0.063 -0.299 0.765
## ef 0.032 0.064 0.503 0.615
## gh 0.119 0.158 0.749 0.454
## total 1.066 0.784 1.359 0.174semPaths(fit)
Total dairy
model_total <- ' # direct effect
BMSi ~ i*mod
# mediator
IL6 ~ a*mod
TNFa ~ c*mod
IL1B ~ e*mod
CRP ~ g*mod
BMSi ~ b*IL6
BMSi ~ d*TNFa
BMSi ~ f*IL1B
BMSi~ h*CRP
# indirect effect (a*b)
ab := a*b
cd := c*d
ef := e*f
gh :=g*h
# total effect
total := i + (a*b) +(c*d) +(e*f) +(g*h)
'
fit <- sem(model_total, data = db)
summary(fit, fit.measures=TRUE, standardized=TRUE)## lavaan 0.6-18 ended normally after 1 iteration
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 14
##
## Used Total
## Number of observations 151 163
##
## Model Test User Model:
##
## Test statistic 8.443
## Degrees of freedom 6
## P-value (Chi-square) 0.207
##
## Model Test Baseline Model:
##
## Test statistic 21.448
## Degrees of freedom 15
## P-value 0.123
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.621
## Tucker-Lewis Index (TLI) 0.053
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -2694.331
## Loglikelihood unrestricted model (H1) -2690.110
##
## Akaike (AIC) 5416.662
## Bayesian (BIC) 5458.904
## Sample-size adjusted Bayesian (SABIC) 5414.596
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.052
## 90 Percent confidence interval - lower 0.000
## 90 Percent confidence interval - upper 0.126
## P-value H_0: RMSEA <= 0.050 0.414
## P-value H_0: RMSEA >= 0.080 0.322
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.050
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## BMSi ~
## mod (i) 1.110 0.797 1.393 0.164 1.110 0.115
## IL6 ~
## mod (a) -0.424 0.446 -0.951 0.341 -0.424 -0.077
## TNFa ~
## mod (c) 0.407 0.698 0.583 0.560 0.407 0.047
## IL1B ~
## mod (e) -1.858 2.622 -0.708 0.479 -1.858 -0.058
## CRP ~
## mod (g) -1.603 0.616 -2.602 0.009 -1.603 -0.207
## BMSi ~
## IL6 (b) -0.122 0.142 -0.864 0.388 -0.122 -0.069
## TNFa (d) -0.027 0.090 -0.295 0.768 -0.027 -0.024
## IL1B (f) -0.018 0.024 -0.740 0.459 -0.018 -0.059
## CRP (h) -0.072 0.102 -0.703 0.482 -0.072 -0.058
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .BMSi 64.525 7.426 8.689 0.000 64.525 0.970
## .IL6 21.311 2.453 8.689 0.000 21.311 0.994
## .TNFa 52.360 6.026 8.689 0.000 52.360 0.998
## .IL1B 738.363 84.976 8.689 0.000 738.363 0.997
## .CRP 40.784 4.694 8.689 0.000 40.784 0.957
##
## Defined Parameters:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## ab 0.052 0.081 0.640 0.522 0.052 0.005
## cd -0.011 0.041 -0.263 0.792 -0.011 -0.001
## ef 0.033 0.065 0.512 0.609 0.033 0.003
## gh 0.115 0.170 0.679 0.497 0.115 0.012
## total 1.300 0.780 1.666 0.096 1.300 0.134semPaths(fit)
Adjusted milk as predictor, BMSi as response; IL6, TNFa, IL1B, CRP as individual mediators
model_milk_adj <- ' # direct effect
BMSi ~ i*milk + age_final + female_b2 + PA_SCORE_b2 + vitd_top + BMI_b2 + alcohol_freq_8yr + diabetes_bone2 + PTH_8yr
# mediator
IL6 ~ a*milk
TNFa ~ c*milk
IL1B ~ e*milk
CRP ~ g*milk
BMSi ~ b*IL6
BMSi ~ d*TNFa
BMSi ~ f*IL1B
BMSi ~ h*CRP
# indirect effect (a*b)
ab := a*b
cd := c*d
ef := e*f
gh := g*h
# total effect
total := i + (a*b) +(c*d) +(e*f) +(g*h)
'
fit_milk_adj <- sem(model_milk_adj, data = db)
summary(fit_milk_adj, fit.measures=TRUE, standardized=TRUE, ci=TRUE)## lavaan 0.6-18 ended normally after 1 iteration
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 22
##
## Used Total
## Number of observations 129 163
##
## Model Test User Model:
##
## Test statistic 66.495
## Degrees of freedom 38
## P-value (Chi-square) 0.003
##
## Model Test Baseline Model:
##
## Test statistic 89.665
## Degrees of freedom 55
## P-value 0.002
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.178
## Tucker-Lewis Index (TLI) -0.190
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -2310.245
## Loglikelihood unrestricted model (H1) -2276.997
##
## Akaike (AIC) 4664.489
## Bayesian (BIC) 4727.405
## Sample-size adjusted Bayesian (SABIC) 4657.826
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.076
## 90 Percent confidence interval - lower 0.044
## 90 Percent confidence interval - upper 0.106
## P-value H_0: RMSEA <= 0.050 0.082
## P-value H_0: RMSEA >= 0.080 0.443
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.069
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## BMSi ~
## milk (i) 2.113 0.957 2.208 0.027 0.237 3.989
## age_final -0.188 0.115 -1.626 0.104 -0.414 0.039
## female_b2 -0.090 1.690 -0.053 0.958 -3.403 3.223
## PA_SCORE_2 0.139 0.130 1.071 0.284 -0.116 0.394
## vitd_top -0.067 0.125 -0.538 0.591 -0.313 0.178
## BMI_b2 -0.284 0.129 -2.202 0.028 -0.536 -0.031
## alchl_fr_8 -0.371 1.308 -0.284 0.777 -2.934 2.192
## diabts_bn2 -0.057 1.429 -0.040 0.968 -2.859 2.744
## PTH_8yr 0.015 0.018 0.870 0.384 -0.019 0.050
## IL6 ~
## milk (a) -0.524 0.554 -0.946 0.344 -1.610 0.562
## TNFa ~
## milk (c) 0.405 0.828 0.489 0.625 -1.219 2.029
## IL1B ~
## milk (e) -3.660 3.019 -1.212 0.225 -9.578 2.257
## CRP ~
## milk (g) -1.429 0.734 -1.948 0.051 -2.867 0.009
## BMSi ~
## IL6 (b) -0.167 0.139 -1.203 0.229 -0.439 0.105
## TNFa (d) -0.063 0.093 -0.675 0.500 -0.244 0.119
## IL1B (f) -0.012 0.025 -0.489 0.625 -0.062 0.037
## CRP (h) -0.017 0.105 -0.163 0.870 -0.222 0.188
## Std.lv Std.all
##
## 2.113 0.199
## -0.188 -0.146
## -0.090 -0.005
## 0.139 0.097
## -0.067 -0.047
## -0.284 -0.194
## -0.371 -0.025
## -0.057 -0.003
## 0.015 0.080
##
## -0.524 -0.083
##
## 0.405 0.043
##
## -3.660 -0.106
##
## -1.429 -0.169
##
## -0.167 -0.099
## -0.063 -0.056
## -0.012 -0.041
## -0.017 -0.014
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## .BMSi 60.442 7.526 8.031 0.000 45.692 75.193
## .IL6 24.348 3.032 8.031 0.000 18.406 30.289
## .TNFa 54.423 6.776 8.031 0.000 41.141 67.704
## .IL1B 722.966 90.020 8.031 0.000 546.531 899.402
## .CRP 42.696 5.316 8.031 0.000 32.276 53.115
## Std.lv Std.all
## 60.442 0.876
## 24.348 0.993
## 54.423 0.998
## 722.966 0.989
## 42.696 0.971
##
## Defined Parameters:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## ab 0.087 0.118 0.744 0.457 -0.143 0.318
## cd -0.025 0.064 -0.396 0.692 -0.151 0.100
## ef 0.046 0.100 0.454 0.650 -0.151 0.242
## gh 0.024 0.150 0.162 0.871 -0.270 0.319
## total 2.245 0.944 2.378 0.017 0.395 4.095
## Std.lv Std.all
## 0.087 0.008
## -0.025 -0.002
## 0.046 0.004
## 0.024 0.002
## 2.245 0.212semPaths(fit_milk_adj)
Adjusted milk with log tranformed mediators(without this tranformation, the variances are extremely high)
model_milk_adj_log <- ' # direct effect
BMSi ~ i*milk + age_final + female_b2 + PA_SCORE_b2 + vitd_top + BMI_b2 + alcohol_freq_8yr + diabetes_bone2 + PTH_8yr
# mediator
log_IL6 ~ a*milk
log_tnf ~ c*milk
log_il1B ~ e*milk
log_crp ~ g*milk
BMSi ~ b*log_IL6
BMSi ~ d*log_tnf
BMSi ~ f*log_il1B
BMSi ~ h*log_crp
# indirect effect (a*b)
ab := a*b
cd := c*d
ef := e*f
gh := g*h
# total effect
total := i + (a*b) +(c*d) +(e*f) +(g*h)
'
fit_milk_adj_log <- sem(model_milk_adj_log, data = db)
summary(fit_milk_adj_log, fit.measures=TRUE, standardized=TRUE, ci=TRUE)## lavaan 0.6-18 ended normally after 1 iteration
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 22
##
## Used Total
## Number of observations 129 163
##
## Model Test User Model:
##
## Test statistic 64.192
## Degrees of freedom 38
## P-value (Chi-square) 0.005
##
## Model Test Baseline Model:
##
## Test statistic 94.414
## Degrees of freedom 55
## P-value 0.001
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.335
## Tucker-Lewis Index (TLI) 0.038
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -1109.626
## Loglikelihood unrestricted model (H1) -1077.530
##
## Akaike (AIC) 2263.251
## Bayesian (BIC) 2326.167
## Sample-size adjusted Bayesian (SABIC) 2256.588
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.073
## 90 Percent confidence interval - lower 0.040
## 90 Percent confidence interval - upper 0.103
## P-value H_0: RMSEA <= 0.050 0.111
## P-value H_0: RMSEA >= 0.080 0.378
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.070
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## BMSi ~
## milk (i) 2.062 0.942 2.188 0.029 0.214 3.909
## age_final -0.215 0.113 -1.903 0.057 -0.436 0.006
## female_b2 0.104 1.656 0.063 0.950 -3.141 3.348
## PA_SCORE_2 0.177 0.127 1.391 0.164 -0.073 0.427
## vitd_top -0.046 0.123 -0.377 0.706 -0.287 0.194
## BMI_b2 -0.315 0.126 -2.497 0.013 -0.562 -0.068
## alchl_fr_8 -0.654 1.281 -0.510 0.610 -3.164 1.856
## diabts_bn2 -0.105 1.400 -0.075 0.940 -2.848 2.639
## PTH_8yr 0.010 0.017 0.590 0.555 -0.024 0.044
## log_IL6 ~
## milk (a) -0.104 0.104 -0.996 0.319 -0.307 0.100
## log_tnf ~
## milk (c) 0.034 0.059 0.578 0.564 -0.081 0.149
## log_il1B ~
## milk (e) -0.190 0.105 -1.814 0.070 -0.395 0.015
## log_crp ~
## milk (g) -0.275 0.147 -1.864 0.062 -0.563 0.014
## BMSi ~
## log_IL6 (b) -1.633 0.724 -2.257 0.024 -3.051 -0.215
## log_tnf (d) -0.976 1.282 -0.762 0.446 -3.488 1.536
## log_il1B (f) -0.931 0.719 -1.296 0.195 -2.340 0.478
## log_crp (h) 0.665 0.511 1.301 0.193 -0.337 1.667
## Std.lv Std.all
##
## 2.062 0.192
## -0.215 -0.165
## 0.104 0.005
## 0.177 0.122
## -0.046 -0.032
## -0.315 -0.213
## -0.654 -0.043
## -0.105 -0.006
## 0.010 0.052
##
## -0.104 -0.087
##
## 0.034 0.051
##
## -0.190 -0.158
##
## -0.275 -0.162
##
## -1.633 -0.181
## -0.976 -0.061
## -0.931 -0.105
## 0.665 0.105
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## .BMSi 57.971 7.218 8.031 0.000 43.824 72.119
## .log_IL6 0.858 0.107 8.031 0.000 0.649 1.068
## .log_tnf 0.274 0.034 8.031 0.000 0.207 0.340
## .log_il1B 0.870 0.108 8.031 0.000 0.657 1.082
## .log_crp 1.721 0.214 8.031 0.000 1.301 2.141
## Std.lv Std.all
## 57.971 0.822
## 0.858 0.992
## 0.274 0.997
## 0.870 0.975
## 1.721 0.974
##
## Defined Parameters:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## ab 0.169 0.186 0.911 0.362 -0.195 0.533
## cd -0.033 0.072 -0.460 0.645 -0.174 0.108
## ef 0.177 0.168 1.054 0.292 -0.152 0.506
## gh -0.183 0.171 -1.067 0.286 -0.518 0.153
## total 2.192 0.945 2.319 0.020 0.339 4.045
## Std.lv Std.all
## 0.169 0.016
## -0.033 -0.003
## 0.177 0.017
## -0.183 -0.017
## 2.192 0.205semPaths(fit_milk_adj_log)
Fluid dairy adjusted
model_fluid_adj <- ' # direct effect
BMSi ~ i*fluid + age_final + female_b2 + BMI_b2 + alcohol_freq_8yr + diabetes_bone2 + PTH_8yr
# mediator
IL6 ~ a*fluid
TNFa ~ c*fluid
IL1B ~ e*fluid
CRP ~ g*fluid
BMSi ~ b*IL6
BMSi ~ d*TNFa
BMSi ~ f*IL1B
BMSi ~ h*CRP
# indirect effect (a*b)
ab := a*b
cd := c*d
ef := e*f
gh := g*h
# total effect
total := i + (a*b) +(c*d) +(e*f) +(g*h)
'
fit_fluid_adj <- sem(model_fluid_adj, data = db)
summary(fit_fluid_adj, fit.measures=TRUE, standardized=TRUE, ci=TRUE)## lavaan 0.6-18 ended normally after 1 iteration
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 20
##
## Used Total
## Number of observations 130 163
##
## Model Test User Model:
##
## Test statistic 45.777
## Degrees of freedom 30
## P-value (Chi-square) 0.033
##
## Model Test Baseline Model:
##
## Test statistic 66.074
## Degrees of freedom 45
## P-value 0.022
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.251
## Tucker-Lewis Index (TLI) -0.123
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -2329.073
## Loglikelihood unrestricted model (H1) -2306.185
##
## Akaike (AIC) 4698.146
## Bayesian (BIC) 4755.497
## Sample-size adjusted Bayesian (SABIC) 4692.241
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.064
## 90 Percent confidence interval - lower 0.019
## 90 Percent confidence interval - upper 0.099
## P-value H_0: RMSEA <= 0.050 0.255
## P-value H_0: RMSEA >= 0.080 0.244
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.065
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## BMSi ~
## fluid (i) 1.702 0.893 1.906 0.057 -0.048 3.452
## age_final -0.159 0.116 -1.371 0.170 -0.385 0.068
## female_b2 -0.444 1.709 -0.260 0.795 -3.794 2.906
## BMI_b2 -0.270 0.128 -2.115 0.034 -0.520 -0.020
## alchl_fr_8 -0.482 1.288 -0.374 0.708 -3.007 2.043
## diabts_bn2 0.269 1.443 0.186 0.852 -2.560 3.097
## PTH_8yr 0.022 0.017 1.295 0.195 -0.011 0.056
## IL6 ~
## fluid (a) -0.468 0.515 -0.910 0.363 -1.477 0.540
## TNFa ~
## fluid (c) 0.437 0.772 0.566 0.572 -1.077 1.950
## IL1B ~
## fluid (e) -3.135 2.808 -1.116 0.264 -8.639 2.370
## CRP ~
## fluid (g) -1.335 0.681 -1.959 0.050 -2.670 0.000
## BMSi ~
## IL6 (b) -0.127 0.140 -0.906 0.365 -0.403 0.148
## TNFa (d) -0.077 0.094 -0.822 0.411 -0.260 0.107
## IL1B (f) -0.014 0.026 -0.550 0.582 -0.065 0.036
## CRP (h) -0.045 0.106 -0.429 0.668 -0.253 0.162
## Std.lv Std.all
##
## 1.702 0.172
## -0.159 -0.124
## -0.444 -0.023
## -0.270 -0.184
## -0.482 -0.032
## 0.269 0.016
## 0.022 0.114
##
## -0.468 -0.080
##
## 0.437 0.050
##
## -3.135 -0.097
##
## -1.335 -0.169
##
## -0.127 -0.076
## -0.077 -0.068
## -0.014 -0.046
## -0.045 -0.036
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## .BMSi 62.098 7.702 8.062 0.000 47.002 77.194
## .IL6 24.209 3.003 8.062 0.000 18.324 30.095
## .TNFa 54.502 6.760 8.062 0.000 41.252 67.752
## .IL1B 721.090 89.440 8.062 0.000 545.791 896.390
## .CRP 42.439 5.264 8.062 0.000 32.122 52.756
## Std.lv Std.all
## 62.098 0.900
## 24.209 0.994
## 54.502 0.998
## 721.090 0.991
## 42.439 0.971
##
## Defined Parameters:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## ab 0.060 0.093 0.642 0.521 -0.122 0.242
## cd -0.034 0.072 -0.466 0.641 -0.175 0.108
## ef 0.044 0.090 0.493 0.622 -0.132 0.221
## gh 0.061 0.145 0.419 0.675 -0.223 0.345
## total 1.833 0.880 2.082 0.037 0.107 3.559
## Std.lv Std.all
## 0.060 0.006
## -0.034 -0.003
## 0.044 0.004
## 0.061 0.006
## 1.833 0.185semPaths(fit_fluid_adj)
Fluid dairy adjusted w/ log transformed mediators
model_fluid_adj_log <- ' # direct effect
BMSi ~ i*fluid + age_final + female_b2 + BMI_b2 + alcohol_freq_8yr + diabetes_bone2 + PTH_8yr
# mediator
log_IL6 ~ a*fluid
log_tnf ~ c*fluid
log_il1B ~ e*fluid
log_crp ~ g*fluid
BMSi ~ b*log_IL6
BMSi ~ d*log_tnf
BMSi ~ f*log_il1B
BMSi ~ h*log_crp
# indirect effect (a*b)
ab := a*b
cd := c*d
ef := e*f
gh := g*h
# total effect
total := i + (a*b) +(c*d) +(e*f) +(g*h)
'
fit_fluid_adj_log <- sem(model_fluid_adj_log, data = db)
summary(fit_fluid_adj_log, fit.measures=TRUE, standardized=TRUE, ci=TRUE)## lavaan 0.6-18 ended normally after 1 iteration
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 20
##
## Used Total
## Number of observations 130 163
##
## Model Test User Model:
##
## Test statistic 52.080
## Degrees of freedom 30
## P-value (Chi-square) 0.007
##
## Model Test Baseline Model:
##
## Test statistic 77.604
## Degrees of freedom 45
## P-value 0.002
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.323
## Tucker-Lewis Index (TLI) -0.016
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -1121.111
## Loglikelihood unrestricted model (H1) -1095.071
##
## Akaike (AIC) 2282.222
## Bayesian (BIC) 2339.572
## Sample-size adjusted Bayesian (SABIC) 2276.317
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.075
## 90 Percent confidence interval - lower 0.039
## 90 Percent confidence interval - upper 0.109
## P-value H_0: RMSEA <= 0.050 0.113
## P-value H_0: RMSEA >= 0.080 0.436
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.072
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## BMSi ~
## fluid (i) 1.698 0.881 1.926 0.054 -0.030 3.425
## age_final -0.184 0.114 -1.614 0.107 -0.407 0.039
## female_b2 -0.256 1.682 -0.152 0.879 -3.552 3.040
## BMI_b2 -0.308 0.126 -2.450 0.014 -0.554 -0.061
## alchl_fr_8 -0.755 1.267 -0.595 0.552 -3.239 1.729
## diabts_bn2 0.264 1.420 0.186 0.853 -2.519 3.046
## PTH_8yr 0.019 0.017 1.132 0.258 -0.014 0.052
## log_IL6 ~
## fluid (a) -0.083 0.097 -0.851 0.395 -0.273 0.108
## log_tnf ~
## fluid (c) 0.039 0.055 0.710 0.478 -0.069 0.147
## log_il1B ~
## fluid (e) -0.158 0.097 -1.618 0.106 -0.349 0.033
## log_crp ~
## fluid (g) -0.251 0.137 -1.837 0.066 -0.519 0.017
## BMSi ~
## log_IL6 (b) -1.345 0.732 -1.838 0.066 -2.779 0.089
## log_tnf (d) -1.389 1.294 -1.073 0.283 -3.925 1.147
## log_il1B (f) -0.976 0.730 -1.338 0.181 -2.406 0.454
## log_crp (h) 0.448 0.520 0.861 0.389 -0.572 1.467
## Std.lv Std.all
##
## 1.698 0.170
## -0.184 -0.143
## -0.256 -0.013
## -0.308 -0.208
## -0.755 -0.050
## 0.264 0.016
## 0.019 0.097
##
## -0.083 -0.074
##
## 0.039 0.062
##
## -0.158 -0.140
##
## -0.251 -0.159
##
## -1.345 -0.150
## -1.389 -0.087
## -0.976 -0.110
## 0.448 0.071
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## .BMSi 60.101 7.455 8.062 0.000 45.490 74.712
## .log_IL6 0.864 0.107 8.062 0.000 0.654 1.074
## .log_tnf 0.276 0.034 8.062 0.000 0.209 0.343
## .log_il1B 0.869 0.108 8.062 0.000 0.658 1.080
## .log_crp 1.710 0.212 8.062 0.000 1.294 2.125
## Std.lv Std.all
## 60.101 0.860
## 0.864 0.994
## 0.276 0.996
## 0.869 0.980
## 1.710 0.975
##
## Defined Parameters:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## ab 0.111 0.144 0.772 0.440 -0.171 0.393
## cd -0.054 0.092 -0.592 0.554 -0.234 0.125
## ef 0.154 0.149 1.031 0.302 -0.139 0.447
## gh -0.112 0.144 -0.779 0.436 -0.395 0.170
## total 1.796 0.881 2.039 0.041 0.070 3.523
## Std.lv Std.all
## 0.111 0.011
## -0.054 -0.005
## 0.154 0.015
## -0.112 -0.011
## 1.796 0.180semPaths(fit_fluid_adj_log)
Total dairy adjusted
model_total_adj <- ' # direct effect
BMSi ~ i*mod + age_final + female_b2 + BMI_b2 + alcohol_freq_8yr + diabetes_bone2 + PTH_8yr
# mediator
IL6 ~ a*mod
TNFa ~ c*mod
IL1B ~ e*mod
CRP ~ g*mod
BMSi ~ b*IL6
BMSi ~ d*TNFa
BMSi ~ f*IL1B
BMSi ~ h*CRP
# indirect effect (a*b)
ab := a*b
cd := c*d
ef := e*f
gh := g*h
# total effect
total := i + (a*b) +(c*d) +(e*f) +(g*h)
'
fit_total_adj <- sem(model_total_adj, data = db)
summary(fit_total_adj,fit.measures=TRUE, standardized=TRUE, ci=TRUE)## lavaan 0.6-18 ended normally after 9 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 20
##
## Used Total
## Number of observations 130 163
##
## Model Test User Model:
##
## Test statistic 45.543
## Degrees of freedom 30
## P-value (Chi-square) 0.034
##
## Model Test Baseline Model:
##
## Test statistic 66.804
## Degrees of freedom 45
## P-value 0.019
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.287
## Tucker-Lewis Index (TLI) -0.069
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -2328.592
## Loglikelihood unrestricted model (H1) -2305.820
##
## Akaike (AIC) 4697.183
## Bayesian (BIC) 4754.534
## Sample-size adjusted Bayesian (SABIC) 4691.278
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.063
## 90 Percent confidence interval - lower 0.018
## 90 Percent confidence interval - upper 0.098
## P-value H_0: RMSEA <= 0.050 0.262
## P-value H_0: RMSEA >= 0.080 0.237
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.065
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## BMSi ~
## mod (i) 1.848 0.904 2.045 0.041 0.077 3.619
## age_final -0.154 0.115 -1.340 0.180 -0.379 0.071
## female_b2 -0.579 1.714 -0.338 0.736 -3.938 2.781
## BMI_b2 -0.260 0.128 -2.040 0.041 -0.511 -0.010
## alchl_fr_8 -0.391 1.292 -0.303 0.762 -2.923 2.140
## diabts_bn2 0.261 1.440 0.182 0.856 -2.560 3.083
## PTH_8yr 0.023 0.017 1.321 0.186 -0.011 0.056
## IL6 ~
## mod (a) -0.381 0.519 -0.734 0.463 -1.398 0.636
## TNFa ~
## mod (c) 0.236 0.778 0.303 0.762 -1.290 1.761
## IL1B ~
## mod (e) -3.363 2.826 -1.190 0.234 -8.903 2.176
## CRP ~
## mod (g) -1.473 0.684 -2.154 0.031 -2.814 -0.133
## BMSi ~
## IL6 (b) -0.129 0.140 -0.925 0.355 -0.404 0.145
## TNFa (d) -0.072 0.093 -0.767 0.443 -0.255 0.111
## IL1B (f) -0.013 0.026 -0.507 0.612 -0.063 0.037
## CRP (h) -0.041 0.106 -0.382 0.703 -0.249 0.168
## Std.lv Std.all
##
## 1.848 0.185
## -0.154 -0.120
## -0.579 -0.031
## -0.260 -0.177
## -0.391 -0.026
## 0.261 0.016
## 0.023 0.116
##
## -0.381 -0.064
##
## 0.236 0.027
##
## -3.363 -0.104
##
## -1.473 -0.186
##
## -0.129 -0.077
## -0.072 -0.064
## -0.013 -0.042
## -0.041 -0.032
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## .BMSi 61.842 7.671 8.062 0.000 46.808 76.876
## .IL6 24.263 3.009 8.062 0.000 18.365 30.161
## .TNFa 54.598 6.772 8.062 0.000 41.325 67.871
## .IL1B 720.157 89.324 8.062 0.000 545.084 895.230
## .CRP 42.187 5.233 8.062 0.000 31.931 52.442
## Std.lv Std.all
## 61.842 0.896
## 24.263 0.996
## 54.598 0.999
## 720.157 0.989
## 42.187 0.966
##
## Defined Parameters:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## ab 0.049 0.086 0.575 0.565 -0.119 0.217
## cd -0.017 0.060 -0.282 0.778 -0.134 0.100
## ef 0.044 0.094 0.467 0.641 -0.140 0.228
## gh 0.060 0.159 0.376 0.707 -0.252 0.371
## total 1.984 0.889 2.231 0.026 0.241 3.727
## Std.lv Std.all
## 0.049 0.005
## -0.017 -0.002
## 0.044 0.004
## 0.060 0.006
## 1.984 0.199semPaths(fit_total_adj)
##total adjusted with log transformed mediators
model_total_adj_log <- ' # direct effect
BMSi ~ i*mod + age_final + female_b2 + BMI_b2 + alcohol_freq_8yr + diabetes_bone2 + PTH_8yr
# mediator
log_IL6 ~ a*mod
log_tnf ~ c*mod
log_il1B ~ e*mod
log_crp ~ g*mod
BMSi ~ b*log_IL6
BMSi ~ d*log_tnf
BMSi ~ f*log_il1B
BMSi ~ h*log_crp
# indirect effect (a*b)
ab := a*b
cd := c*d
ef := e*f
gh := g*h
# total effect
total := i + (a*b) +(c*d) +(e*f) +(g*h)
'
fit_total_adj_log <- sem(model_total_adj_log, data = db)
summary(fit_total_adj_log,fit.measures=TRUE, standardized=TRUE, ci=TRUE)## lavaan 0.6-18 ended normally after 1 iteration
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 20
##
## Used Total
## Number of observations 130 163
##
## Model Test User Model:
##
## Test statistic 51.790
## Degrees of freedom 30
## P-value (Chi-square) 0.008
##
## Model Test Baseline Model:
##
## Test statistic 78.790
## Degrees of freedom 45
## P-value 0.001
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.355
## Tucker-Lewis Index (TLI) 0.033
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -1120.373
## Loglikelihood unrestricted model (H1) -1094.478
##
## Akaike (AIC) 2280.747
## Bayesian (BIC) 2338.097
## Sample-size adjusted Bayesian (SABIC) 2274.841
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.075
## 90 Percent confidence interval - lower 0.038
## 90 Percent confidence interval - upper 0.108
## P-value H_0: RMSEA <= 0.050 0.118
## P-value H_0: RMSEA >= 0.080 0.427
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.072
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## BMSi ~
## mod (i) 1.841 0.893 2.061 0.039 0.090 3.592
## age_final -0.178 0.113 -1.578 0.115 -0.399 0.043
## female_b2 -0.403 1.686 -0.239 0.811 -3.708 2.903
## BMI_b2 -0.298 0.126 -2.373 0.018 -0.544 -0.052
## alchl_fr_8 -0.666 1.271 -0.524 0.600 -3.157 1.824
## diabts_bn2 0.263 1.416 0.186 0.853 -2.513 3.039
## PTH_8yr 0.019 0.017 1.155 0.248 -0.014 0.052
## log_IL6 ~
## mod (a) -0.083 0.098 -0.844 0.399 -0.274 0.109
## log_tnf ~
## mod (c) 0.034 0.055 0.609 0.542 -0.075 0.142
## log_il1B ~
## mod (e) -0.166 0.098 -1.695 0.090 -0.358 0.026
## log_crp ~
## mod (g) -0.283 0.137 -2.061 0.039 -0.552 -0.014
## BMSi ~
## log_IL6 (b) -1.332 0.730 -1.824 0.068 -2.763 0.099
## log_tnf (d) -1.370 1.291 -1.062 0.288 -3.900 1.159
## log_il1B (f) -0.942 0.729 -1.293 0.196 -2.371 0.486
## log_crp (h) 0.467 0.521 0.897 0.369 -0.553 1.488
## Std.lv Std.all
##
## 1.841 0.183
## -0.178 -0.138
## -0.403 -0.021
## -0.298 -0.202
## -0.666 -0.044
## 0.263 0.016
## 0.019 0.099
##
## -0.083 -0.074
##
## 0.034 0.053
##
## -0.166 -0.147
##
## -0.283 -0.178
##
## -1.332 -0.149
## -1.370 -0.086
## -0.942 -0.106
## 0.467 0.074
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## .BMSi 59.861 7.425 8.062 0.000 45.309 74.413
## .log_IL6 0.864 0.107 8.062 0.000 0.654 1.074
## .log_tnf 0.276 0.034 8.062 0.000 0.209 0.344
## .log_il1B 0.867 0.108 8.062 0.000 0.656 1.078
## .log_crp 1.699 0.211 8.062 0.000 1.286 2.111
## Std.lv Std.all
## 59.861 0.857
## 0.864 0.995
## 0.276 0.997
## 0.867 0.978
## 1.699 0.968
##
## Defined Parameters:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## ab 0.110 0.144 0.766 0.444 -0.171 0.392
## cd -0.046 0.087 -0.528 0.597 -0.218 0.125
## ef 0.157 0.152 1.028 0.304 -0.142 0.455
## gh -0.132 0.161 -0.823 0.411 -0.447 0.183
## total 1.929 0.890 2.168 0.030 0.185 3.673
## Std.lv Std.all
## 0.110 0.011
## -0.046 -0.005
## 0.157 0.016
## -0.132 -0.013
## 1.929 0.192semPaths(fit_total_adj_log)
No-fat as predictor var, TBS as response var; IL6, TNFa, IL1B, CRP as individual mediators
model_skim_TBS <- ' # direct effect
TBSL1L2L3L4_final ~ i*skim
# mediator
IL6 ~ a*skim
TNFa ~ c*skim
IL1B ~ e*skim
CRP ~ g*skim
TBSL1L2L3L4_final ~ b*IL6
TBSL1L2L3L4_final ~ d*TNFa
TBSL1L2L3L4_final ~ f*IL1B
TBSL1L2L3L4_final ~ h*CRP
# indirect effect (a*b)
ab := a*b
cd := c*d
ef := e*f
gh := g*h
# total effect
total := i + (a*b) +(c*d) +(e*f) +(g*h)
'
fit2_skim <- sem(model_skim_TBS, data = db2)## Warning: lavaan->lav_data_full():
## some observed variances are (at least) a factor 1000 times larger than
## others; use varTable(fit) to investigatesummary(fit2_skim,fit.measures=TRUE, standardized=TRUE, ci=TRUE )## lavaan 0.6-18 ended normally after 34 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 14
##
## Used Total
## Number of observations 396 445
##
## Model Test User Model:
##
## Test statistic 81.283
## Degrees of freedom 6
## P-value (Chi-square) 0.000
##
## Model Test Baseline Model:
##
## Test statistic 93.077
## Degrees of freedom 15
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.036
## Tucker-Lewis Index (TLI) -1.411
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -5940.723
## Loglikelihood unrestricted model (H1) -5900.081
##
## Akaike (AIC) 11909.445
## Bayesian (BIC) 11965.185
## Sample-size adjusted Bayesian (SABIC) 11920.763
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.178
## 90 Percent confidence interval - lower 0.145
## 90 Percent confidence interval - upper 0.213
## P-value H_0: RMSEA <= 0.050 0.000
## P-value H_0: RMSEA >= 0.080 1.000
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.099
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## TBSL1L2L3L4_final ~
## skim (i) -0.046 0.018 -2.518 0.012 -0.081 -0.010
## IL6 ~
## skim (a) 0.642 0.693 0.927 0.354 -0.716 2.000
## TNFa ~
## skim (c) 0.241 0.871 0.277 0.782 -1.466 1.948
## IL1B ~
## skim (e) 0.231 4.620 0.050 0.960 -8.824 9.287
## CRP ~
## skim (g) -1.894 1.344 -1.409 0.159 -4.528 0.741
## TBSL1L2L3L4_final ~
## IL6 (b) 0.000 0.001 0.314 0.753 -0.002 0.003
## TNFa (d) -0.001 0.001 -0.567 0.571 -0.003 0.001
## IL1B (f) 0.000 0.000 1.465 0.143 -0.000 0.001
## CRP (h) -0.000 0.001 -0.647 0.518 -0.002 0.001
## Std.lv Std.all
##
## -0.046 -0.126
##
## 0.642 0.047
##
## 0.241 0.014
##
## 0.231 0.003
##
## -1.894 -0.071
##
## 0.000 0.016
## -0.001 -0.028
## 0.000 0.073
## -0.000 -0.032
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## .TBSL1L2L3L4_fn 0.023 0.002 14.071 0.000 0.020 0.026
## .IL6 33.309 2.367 14.071 0.000 28.669 37.949
## .TNFa 52.641 3.741 14.071 0.000 45.308 59.973
## .IL1B 1481.066 105.255 14.071 0.000 1274.770 1687.361
## .CRP 125.373 8.910 14.071 0.000 107.910 142.836
## Std.lv Std.all
## 0.023 0.978
## 33.309 0.998
## 52.641 1.000
## 1481.066 1.000
## 125.373 0.995
##
## Defined Parameters:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## ab 0.000 0.001 0.298 0.766 -0.001 0.002
## cd -0.000 0.001 -0.249 0.804 -0.001 0.001
## ef 0.000 0.001 0.050 0.960 -0.003 0.003
## gh 0.001 0.001 0.588 0.557 -0.002 0.004
## total -0.045 0.018 -2.462 0.014 -0.080 -0.009
## Std.lv Std.all
## 0.000 0.001
## -0.000 -0.000
## 0.000 0.000
## 0.001 0.002
## -0.045 -0.123semPaths(fit2_skim)
###Adjusted skim
model_skim_adj_TBS <- ' # direct effect
TBSL1L2L3L4_final ~ i*skim + age_final + female_b2 + vitd_top + BMI_b2 + alcohol_freq_8yr + diabetes_bone2 + bone6f_b2
# mediator
IL6 ~ a*skim
TNFa ~ c*skim
IL1B ~ e*skim
CRP ~ g*skim
TBSL1L2L3L4_final ~ b*IL6
TBSL1L2L3L4_final ~ d*TNFa
TBSL1L2L3L4_final ~ f*IL1B
TBSL1L2L3L4_final ~ h*CRP
# indirect effect (a*b)
ab := a*b
cd := c*d
ef := e*f
gh := g*h
# total effect
total := i + (a*b) +(c*d) +(e*f) +(g*h)
'
fit2_skim_adj <- sem(model_skim_adj_TBS, data = db2)## Warning: lavaan->lav_data_full():
## some observed variances are (at least) a factor 1000 times larger than
## others; use varTable(fit) to investigatesummary(fit2_skim_adj,fit.measures=TRUE, standardized=TRUE, ci=TRUE )## lavaan 0.6-18 ended normally after 78 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 21
##
## Used Total
## Number of observations 362 445
##
## Model Test User Model:
##
## Test statistic 116.466
## Degrees of freedom 34
## P-value (Chi-square) 0.000
##
## Model Test Baseline Model:
##
## Test statistic 143.150
## Degrees of freedom 50
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.115
## Tucker-Lewis Index (TLI) -0.302
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -5447.407
## Loglikelihood unrestricted model (H1) NA
##
## Akaike (AIC) 10936.813
## Bayesian (BIC) 11018.538
## Sample-size adjusted Bayesian (SABIC) 10951.914
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.082
## 90 Percent confidence interval - lower 0.066
## 90 Percent confidence interval - upper 0.098
## P-value H_0: RMSEA <= 0.050 0.001
## P-value H_0: RMSEA >= 0.080 0.593
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.061
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## TBSL1L2L3L4_final ~
## skim (i) -0.039 0.019 -2.086 0.037 -0.076 -0.002
## age_final -0.000 0.001 -0.094 0.925 -0.002 0.002
## female_b2 -0.015 0.020 -0.768 0.442 -0.053 0.023
## vitd_top -0.001 0.001 -0.507 0.612 -0.003 0.002
## BMI_b2 -0.002 0.001 -1.954 0.051 -0.005 0.000
## alchl_fr_8 0.001 0.015 0.083 0.934 -0.028 0.031
## diabts_bn2 -0.033 0.016 -2.007 0.045 -0.065 -0.001
## bone6f_b2 -0.056 0.024 -2.342 0.019 -0.103 -0.009
## IL6 ~
## skim (a) 0.637 0.740 0.861 0.389 -0.813 2.087
## TNFa ~
## skim (c) 0.328 0.917 0.357 0.721 -1.470 2.125
## IL1B ~
## skim (e) 1.156 4.598 0.251 0.802 -7.856 10.167
## CRP ~
## skim (g) -1.888 1.412 -1.337 0.181 -4.655 0.879
## TBSL1L2L3L4_final ~
## IL6 (b) 0.000 0.001 0.165 0.869 -0.002 0.003
## TNFa (d) -0.000 0.001 -0.198 0.843 -0.002 0.002
## IL1B (f) 0.000 0.000 1.084 0.278 -0.000 0.001
## CRP (h) -0.000 0.001 -0.190 0.850 -0.001 0.001
## Std.lv Std.all
##
## -0.039 -0.108
## -0.000 -0.005
## -0.015 -0.041
## -0.001 -0.026
## -0.002 -0.105
## 0.001 0.004
## -0.033 -0.105
## -0.056 -0.121
##
## 0.637 0.045
##
## 0.328 0.019
##
## 1.156 0.013
##
## -1.888 -0.070
##
## 0.000 0.008
## -0.000 -0.010
## 0.000 0.055
## -0.000 -0.010
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## .TBSL1L2L3L4_fn 0.022 0.002 13.454 0.000 0.019 0.026
## .IL6 35.996 2.676 13.454 0.000 30.752 41.240
## .TNFa 55.346 4.114 13.454 0.000 47.283 63.409
## .IL1B 1390.927 103.387 13.454 0.000 1188.293 1593.562
## .CRP 131.141 9.748 13.454 0.000 112.036 150.246
## Std.lv Std.all
## 0.022 0.938
## 35.996 0.998
## 55.346 1.000
## 1390.927 1.000
## 131.141 0.995
##
## Defined Parameters:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## ab 0.000 0.001 0.162 0.871 -0.002 0.002
## cd -0.000 0.000 -0.173 0.863 -0.001 0.001
## ef 0.000 0.001 0.245 0.807 -0.002 0.002
## gh 0.000 0.001 0.188 0.851 -0.002 0.003
## total -0.038 0.019 -2.060 0.039 -0.075 -0.002
## Std.lv Std.all
## 0.000 0.000
## -0.000 -0.000
## 0.000 0.001
## 0.000 0.001
## -0.038 -0.106semPaths(fit2_skim_adj)
No-fat(skim) dichotomized (since right-skewed) as predictor var, TBS as response var; IL6, TNFa, IL1B, CRP as individual mediators
model_skim_dichot_TBS <- ' # direct effect
TBSL1L2L3L4_final ~ i*skim_dichot
# mediator
IL6 ~ a*skim_dichot
TNFa ~ c*skim_dichot
IL1B ~ e*skim_dichot
CRP ~ g*skim_dichot
TBSL1L2L3L4_final ~ b*IL6
TBSL1L2L3L4_final ~ d*TNFa
TBSL1L2L3L4_final ~ f*IL1B
TBSL1L2L3L4_final ~ h*CRP
# indirect effect (a*b)
ab := a*b
cd := c*d
ef := e*f
gh := g*h
# total effect
total := i + (a*b) +(c*d) +(e*f) +(g*h)
'
fit2_skim_dichot <- sem(model_skim_dichot_TBS, data = db2)## Warning: lavaan->lav_data_full():
## some observed variances are (at least) a factor 1000 times larger than
## others; use varTable(fit) to investigatesummary(fit2_skim_dichot,fit.measures=TRUE, standardized=TRUE, ci=TRUE )## lavaan 0.6-18 ended normally after 47 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 14
##
## Used Total
## Number of observations 396 445
##
## Model Test User Model:
##
## Test statistic 79.433
## Degrees of freedom 6
## P-value (Chi-square) 0.000
##
## Model Test Baseline Model:
##
## Test statistic 83.302
## Degrees of freedom 15
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.000
## Tucker-Lewis Index (TLI) -1.688
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -5944.685
## Loglikelihood unrestricted model (H1) -5904.968
##
## Akaike (AIC) 11917.370
## Bayesian (BIC) 11973.110
## Sample-size adjusted Bayesian (SABIC) 11928.688
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.176
## 90 Percent confidence interval - lower 0.143
## 90 Percent confidence interval - upper 0.211
## P-value H_0: RMSEA <= 0.050 0.000
## P-value H_0: RMSEA >= 0.080 1.000
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.098
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## TBSL1L2L3L4_final ~
## skim_dicht (i) 0.060 0.152 0.393 0.694 -0.238 0.358
## IL6 ~
## skim_dicht (a) 1.661 5.784 0.287 0.774 -9.676 12.998
## TNFa ~
## skim_dicht (c) 4.146 7.262 0.571 0.568 -10.088 18.380
## IL1B ~
## skim_dicht (e) 31.606 38.501 0.821 0.412 -43.854 107.067
## CRP ~
## skim_dicht (g) 1.490 11.239 0.133 0.895 -20.538 23.518
## TBSL1L2L3L4_final ~
## IL6 (b) 0.000 0.001 0.096 0.924 -0.002 0.003
## TNFa (d) -0.001 0.001 -0.623 0.533 -0.003 0.001
## IL1B (f) 0.000 0.000 1.435 0.151 -0.000 0.001
## CRP (h) -0.000 0.001 -0.375 0.707 -0.002 0.001
## Std.lv Std.all
##
## 0.060 0.020
##
## 1.661 0.014
##
## 4.146 0.029
##
## 31.606 0.041
##
## 1.490 0.007
##
## 0.000 0.005
## -0.001 -0.031
## 0.000 0.072
## -0.000 -0.019
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## .TBSL1L2L3L4_fn 0.023 0.002 14.071 0.000 0.020 0.026
## .IL6 33.374 2.372 14.071 0.000 28.726 38.023
## .TNFa 52.607 3.739 14.071 0.000 45.279 59.935
## .IL1B 1478.570 105.077 14.071 0.000 1272.622 1684.518
## .CRP 125.996 8.954 14.071 0.000 108.446 143.546
## Std.lv Std.all
## 0.023 0.993
## 33.374 1.000
## 52.607 0.999
## 1478.570 0.998
## 125.996 1.000
##
## Defined Parameters:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## ab 0.000 0.002 0.091 0.928 -0.004 0.005
## cd -0.003 0.006 -0.421 0.674 -0.015 0.010
## ef 0.009 0.013 0.713 0.476 -0.016 0.034
## gh -0.000 0.003 -0.125 0.901 -0.006 0.006
## total 0.066 0.152 0.433 0.665 -0.233 0.365
## Std.lv Std.all
## 0.000 0.000
## -0.003 -0.001
## 0.009 0.003
## -0.000 -0.000
## 0.066 0.022semPaths(fit2_skim_dichot)
#skim_dichot adjusted with TBS
model_skim_dichot_adj_TBS <- ' # direct effect
TBSL1L2L3L4_final ~ i*skim_dichot + age_final + female_b2 + vitd_top + BMI_b2 + alcohol_freq_8yr + diabetes_bone2 + bone6f_b2
# mediator
IL6 ~ a*skim_dichot
TNFa ~ c*skim_dichot
IL1B ~ e*skim_dichot
CRP ~ g*skim_dichot
TBSL1L2L3L4_final ~ b*IL6
TBSL1L2L3L4_final ~ d*TNFa
TBSL1L2L3L4_final ~ f*IL1B
TBSL1L2L3L4_final ~ h*CRP
# indirect effect (a*b)
ab := a*b
cd := c*d
ef := e*f
gh := g*h
# total effect
total := i + (a*b) +(c*d) +(e*f) +(g*h)
'
fit2_skim_dichot_adj <- sem(model_skim_dichot_adj_TBS, data = db2)## Warning: lavaan->lav_data_full():
## some observed variances are (at least) a factor 1000 times larger than
## others; use varTable(fit) to investigatesummary(fit2_skim_dichot_adj,fit.measures=TRUE, standardized=TRUE, ci=TRUE )## lavaan 0.6-18 ended normally after 65 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 21
##
## Used Total
## Number of observations 362 445
##
## Model Test User Model:
##
## Test statistic 114.280
## Degrees of freedom 34
## P-value (Chi-square) 0.000
##
## Model Test Baseline Model:
##
## Test statistic 135.301
## Degrees of freedom 50
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.059
## Tucker-Lewis Index (TLI) -0.384
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -5450.238
## Loglikelihood unrestricted model (H1) NA
##
## Akaike (AIC) 10942.475
## Bayesian (BIC) 11024.200
## Sample-size adjusted Bayesian (SABIC) 10957.576
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.081
## 90 Percent confidence interval - lower 0.065
## 90 Percent confidence interval - upper 0.097
## P-value H_0: RMSEA <= 0.050 0.001
## P-value H_0: RMSEA >= 0.080 0.550
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.061
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## TBSL1L2L3L4_final ~
## skim_dicht (i) 0.074 0.151 0.488 0.625 -0.223 0.371
## age_final -0.000 0.001 -0.108 0.914 -0.002 0.002
## female_b2 -0.018 0.020 -0.916 0.359 -0.057 0.021
## vitd_top -0.001 0.001 -0.658 0.511 -0.004 0.002
## BMI_b2 -0.003 0.001 -1.966 0.049 -0.005 -0.000
## alchl_fr_8 0.003 0.015 0.191 0.848 -0.027 0.033
## diabts_bn2 -0.037 0.016 -2.260 0.024 -0.069 -0.005
## bone6f_b2 -0.057 0.024 -2.383 0.017 -0.105 -0.010
## IL6 ~
## skim_dicht (a) 1.745 6.013 0.290 0.772 -10.042 13.531
## TNFa ~
## skim_dicht (c) 4.137 7.448 0.555 0.579 -10.461 18.734
## IL1B ~
## skim_dicht (e) 31.338 37.314 0.840 0.401 -41.796 104.471
## CRP ~
## skim_dicht (g) 1.581 11.496 0.138 0.891 -20.950 24.112
## TBSL1L2L3L4_final ~
## IL6 (b) -0.000 0.001 -0.028 0.977 -0.003 0.003
## TNFa (d) -0.000 0.001 -0.225 0.822 -0.002 0.002
## IL1B (f) 0.000 0.000 1.022 0.307 -0.000 0.001
## CRP (h) 0.000 0.001 0.059 0.953 -0.001 0.001
## Std.lv Std.all
##
## 0.074 0.025
## -0.000 -0.006
## -0.018 -0.049
## -0.001 -0.034
## -0.003 -0.106
## 0.003 0.010
## -0.037 -0.118
## -0.057 -0.124
##
## 1.745 0.015
##
## 4.137 0.029
##
## 31.338 0.044
##
## 1.581 0.007
##
## -0.000 -0.001
## -0.000 -0.012
## 0.000 0.052
## 0.000 0.003
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## .TBSL1L2L3L4_fn 0.023 0.002 13.454 0.000 0.019 0.026
## .IL6 36.062 2.680 13.454 0.000 30.808 41.315
## .TNFa 55.318 4.112 13.454 0.000 47.259 63.377
## .IL1B 1388.476 103.205 13.454 0.000 1186.199 1590.754
## .CRP 131.783 9.795 13.454 0.000 112.584 150.981
## Std.lv Std.all
## 0.023 0.948
## 36.062 1.000
## 55.318 0.999
## 1388.476 0.998
## 131.783 1.000
##
## Defined Parameters:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## ab -0.000 0.002 -0.028 0.977 -0.005 0.004
## cd -0.001 0.005 -0.208 0.835 -0.010 0.008
## ef 0.007 0.010 0.649 0.516 -0.014 0.027
## gh 0.000 0.001 0.054 0.957 -0.002 0.002
## total 0.080 0.151 0.527 0.598 -0.217 0.377
## Std.lv Std.all
## -0.000 -0.000
## -0.001 -0.000
## 0.007 0.002
## 0.000 0.000
## 0.080 0.027semPaths(fit2_skim_dichot_adj)
skim & tbs adjusted with log tranformed inflammatory cytokines (bone6f = Ca supp)
model_skim_TBS_log <- ' # direct effect
TBSL1L2L3L4_final ~ i*skim + age_final + female_b2 + vitd_top + BMI_b2 + alcohol_freq_8yr + diabetes_bone2 + bone6f_b2
# mediator
log_IL6 ~ a*skim
log_tnf ~ c*skim
log_il1B ~ e*skim
log_crp ~ g*skim
TBSL1L2L3L4_final ~ b*log_IL6
TBSL1L2L3L4_final ~ d*log_tnf
TBSL1L2L3L4_final ~ f*log_il1B
TBSL1L2L3L4_final ~ h*log_crp
# indirect effect (a*b)
ab := a*b
cd := c*d
ef := e*f
# total effect
total := i + (a*b) +(c*d) +(e*f) +(g*h)
'
fit_skim_log <- sem(model_skim_TBS_log, data = db2)
summary(fit_skim_log,fit.measures=TRUE, standardized=TRUE, ci=TRUE)## lavaan 0.6-18 ended normally after 46 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 21
##
## Used Total
## Number of observations 362 445
##
## Model Test User Model:
##
## Test statistic 129.948
## Degrees of freedom 34
## P-value (Chi-square) 0.000
##
## Model Test Baseline Model:
##
## Test statistic 160.209
## Degrees of freedom 50
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.129
## Tucker-Lewis Index (TLI) -0.280
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -1720.033
## Loglikelihood unrestricted model (H1) NA
##
## Akaike (AIC) 3482.065
## Bayesian (BIC) 3563.790
## Sample-size adjusted Bayesian (SABIC) 3497.166
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.088
## 90 Percent confidence interval - lower 0.073
## 90 Percent confidence interval - upper 0.105
## P-value H_0: RMSEA <= 0.050 0.000
## P-value H_0: RMSEA >= 0.080 0.813
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.068
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## TBSL1L2L3L4_final ~
## skim (i) -0.041 0.019 -2.198 0.028 -0.078 -0.004
## age_final -0.000 0.001 -0.080 0.936 -0.002 0.002
## female_b2 -0.015 0.020 -0.747 0.455 -0.053 0.024
## vitd_top -0.001 0.001 -0.515 0.607 -0.003 0.002
## BMI_b2 -0.002 0.001 -1.528 0.127 -0.004 0.001
## alchl_fr_8 0.004 0.015 0.288 0.773 -0.025 0.034
## diabts_bn2 -0.032 0.016 -1.954 0.051 -0.064 0.000
## bone6f_b2 -0.053 0.024 -2.218 0.027 -0.100 -0.006
## log_IL6 ~
## skim (a) 0.036 0.136 0.268 0.789 -0.230 0.302
## log_tnf ~
## skim (c) 0.062 0.062 1.002 0.316 -0.060 0.184
## log_il1B ~
## skim (e) -0.051 0.110 -0.465 0.642 -0.267 0.165
## log_crp ~
## skim (g) -0.214 0.160 -1.332 0.183 -0.528 0.101
## TBSL1L2L3L4_final ~
## log_IL6 (b) 0.009 0.007 1.242 0.214 -0.005 0.023
## log_tnf (d) -0.006 0.015 -0.390 0.696 -0.036 0.024
## log_il1B (f) 0.004 0.009 0.426 0.670 -0.013 0.021
## log_crp (h) -0.013 0.006 -2.112 0.035 -0.024 -0.001
## Std.lv Std.all
##
## -0.041 -0.113
## -0.000 -0.004
## -0.015 -0.040
## -0.001 -0.027
## -0.002 -0.082
## 0.004 0.015
## -0.032 -0.102
## -0.053 -0.114
##
## 0.036 0.014
##
## 0.062 0.053
##
## -0.051 -0.024
##
## -0.214 -0.070
##
## 0.009 0.063
## -0.006 -0.020
## 0.004 0.022
## -0.013 -0.107
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## .TBSL1L2L3L4_fn 0.022 0.002 13.454 0.000 0.019 0.025
## .log_IL6 1.210 0.090 13.454 0.000 1.034 1.387
## .log_tnf 0.255 0.019 13.454 0.000 0.218 0.292
## .log_il1B 0.798 0.059 13.454 0.000 0.682 0.914
## .log_crp 1.693 0.126 13.454 0.000 1.447 1.940
## Std.lv Std.all
## 0.022 0.931
## 1.210 1.000
## 0.255 0.997
## 0.798 0.999
## 1.693 0.995
##
## Defined Parameters:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## ab 0.000 0.001 0.262 0.794 -0.002 0.003
## cd -0.000 0.001 -0.364 0.716 -0.002 0.002
## ef -0.000 0.001 -0.314 0.754 -0.001 0.001
## total -0.039 0.019 -2.057 0.040 -0.075 -0.002
## Std.lv Std.all
## 0.000 0.001
## -0.000 -0.001
## -0.000 -0.001
## -0.039 -0.107semPaths(fit_skim_log)
#skim_dichot adjusted with TBS and log transformed mediators
model_skim_dichot_log_adj_TBS <- ' # direct effect
TBSL1L2L3L4_final ~ i*skim_dichot + age_final + female_b2 + vitd_top + BMI_b2 + alcohol_freq_8yr + diabetes_bone2 + bone6f_b2
# mediator
log_IL6 ~ a*skim_dichot
log_tnf ~ c*skim_dichot
log_il1B ~ e*skim_dichot
log_crp ~ g*skim_dichot
TBSL1L2L3L4_final ~ b*log_IL6
TBSL1L2L3L4_final ~ d*log_tnf
TBSL1L2L3L4_final ~ f*log_il1B
TBSL1L2L3L4_final ~ h*log_crp
# indirect effect (a*b)
ab := a*b
cd := c*d
ef := e*f
gh := g*h
# total effect
total := i + (a*b) +(c*d) +(e*f) +(g*h)
'
fit2_skim_dichot_log_adj <- sem(model_skim_dichot_log_adj_TBS, data = db2)
summary(fit2_skim_dichot_log_adj,fit.measures=TRUE, standardized=TRUE, ci=TRUE )## lavaan 0.6-18 ended normally after 44 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 21
##
## Used Total
## Number of observations 362 445
##
## Model Test User Model:
##
## Test statistic 130.759
## Degrees of freedom 34
## P-value (Chi-square) 0.000
##
## Model Test Baseline Model:
##
## Test statistic 155.880
## Degrees of freedom 50
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.086
## Tucker-Lewis Index (TLI) -0.344
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -1722.603
## Loglikelihood unrestricted model (H1) NA
##
## Akaike (AIC) 3487.206
## Bayesian (BIC) 3568.930
## Sample-size adjusted Bayesian (SABIC) 3502.307
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.089
## 90 Percent confidence interval - lower 0.073
## 90 Percent confidence interval - upper 0.105
## P-value H_0: RMSEA <= 0.050 0.000
## P-value H_0: RMSEA >= 0.080 0.823
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.068
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## TBSL1L2L3L4_final ~
## skim_dicht (i) 0.070 0.151 0.463 0.643 -0.226 0.366
## age_final -0.000 0.001 -0.088 0.930 -0.002 0.002
## female_b2 -0.018 0.020 -0.903 0.367 -0.056 0.021
## vitd_top -0.001 0.001 -0.648 0.517 -0.003 0.002
## BMI_b2 -0.002 0.001 -1.554 0.120 -0.004 0.001
## alchl_fr_8 0.006 0.015 0.383 0.702 -0.024 0.036
## diabts_bn2 -0.036 0.016 -2.203 0.028 -0.068 -0.004
## bone6f_b2 -0.054 0.024 -2.266 0.023 -0.101 -0.007
## log_IL6 ~
## skim_dicht (a) 0.075 1.102 0.068 0.946 -2.085 2.234
## log_tnf ~
## skim_dicht (c) 0.393 0.506 0.777 0.437 -0.599 1.385
## log_il1B ~
## skim_dicht (e) 1.186 0.893 1.328 0.184 -0.564 2.935
## log_crp ~
## skim_dicht (g) -0.484 1.306 -0.371 0.711 -3.044 2.076
## TBSL1L2L3L4_final ~
## log_IL6 (b) 0.008 0.007 1.180 0.238 -0.006 0.022
## log_tnf (d) -0.008 0.016 -0.489 0.625 -0.038 0.023
## log_il1B (f) 0.004 0.009 0.416 0.677 -0.014 0.021
## log_crp (h) -0.011 0.006 -1.876 0.061 -0.023 0.001
## Std.lv Std.all
##
## 0.070 0.024
## -0.000 -0.005
## -0.018 -0.049
## -0.001 -0.034
## -0.002 -0.084
## 0.006 0.020
## -0.036 -0.115
## -0.054 -0.118
##
## 0.075 0.004
##
## 0.393 0.041
##
## 1.186 0.070
##
## -0.484 -0.019
##
## 0.008 0.060
## -0.008 -0.025
## 0.004 0.021
## -0.011 -0.096
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## .TBSL1L2L3L4_fn 0.022 0.002 13.454 0.000 0.019 0.026
## .log_IL6 1.211 0.090 13.454 0.000 1.034 1.387
## .log_tnf 0.256 0.019 13.454 0.000 0.218 0.293
## .log_il1B 0.795 0.059 13.454 0.000 0.679 0.910
## .log_crp 1.701 0.126 13.454 0.000 1.453 1.949
## Std.lv Std.all
## 0.022 0.944
## 1.211 1.000
## 0.256 0.998
## 0.795 0.995
## 1.701 1.000
##
## Defined Parameters:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## ab 0.001 0.009 0.068 0.946 -0.018 0.019
## cd -0.003 0.007 -0.414 0.679 -0.017 0.011
## ef 0.004 0.011 0.397 0.691 -0.017 0.026
## gh 0.005 0.015 0.364 0.716 -0.024 0.035
## total 0.078 0.152 0.511 0.610 -0.220 0.375
## Std.lv Std.all
## 0.001 0.000
## -0.003 -0.001
## 0.004 0.001
## 0.005 0.002
## 0.078 0.026semPaths(fit2_skim_dichot_log_adj)
Full fat as predictor, TBS as response, and log transformed mediators
model_fat_TBS <- ' # direct effect
TBSL1L2L3L4_final ~ i*fat
# mediator
log_IL6 ~ a*fat
log_tnf ~ c*fat
log_il1B ~ e*fat
log_crp ~ g*fat
TBSL1L2L3L4_final ~ b*log_IL6
TBSL1L2L3L4_final ~ d*log_tnf
TBSL1L2L3L4_final ~ f*log_il1B
TBSL1L2L3L4_final ~ h*log_crp
# indirect effect (a*b)
ab := a*b
cd := c*d
ef := e*f
# total effect
total := i + (a*b) +(c*d) +(e*f) +(g*h)
'
fit_fat <- sem(model_fat_TBS, data = db2)
summary(fit_fat)## lavaan 0.6-18 ended normally after 31 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 14
##
## Used Total
## Number of observations 396 445
##
## Model Test User Model:
##
## Test statistic 53.030
## Degrees of freedom 6
## P-value (Chi-square) 0.000
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Regressions:
## Estimate Std.Err z-value P(>|z|)
## TBSL1L2L3L4_final ~
## fat (i) 0.014 0.008 1.706 0.088
## log_IL6 ~
## fat (a) -0.123 0.061 -2.032 0.042
## log_tnf ~
## fat (c) -0.013 0.028 -0.458 0.647
## log_il1B ~
## fat (e) -0.017 0.049 -0.356 0.722
## log_crp ~
## fat (g) -0.054 0.071 -0.760 0.447
## TBSL1L2L3L4_final ~
## log_IL6 (b) 0.006 0.007 0.911 0.362
## log_tnf (d) -0.013 0.015 -0.860 0.390
## log_il1B (f) 0.009 0.009 1.038 0.299
## log_crp (h) -0.014 0.006 -2.392 0.017
##
## Variances:
## Estimate Std.Err z-value P(>|z|)
## .TBSL1L2L3L4_fn 0.023 0.002 14.071 0.000
## .log_IL6 1.197 0.085 14.071 0.000
## .log_tnf 0.250 0.018 14.071 0.000
## .log_il1B 0.780 0.055 14.071 0.000
## .log_crp 1.639 0.116 14.071 0.000
##
## Defined Parameters:
## Estimate Std.Err z-value P(>|z|)
## ab -0.001 0.001 -0.831 0.406
## cd 0.000 0.000 0.404 0.686
## ef -0.000 0.000 -0.337 0.736
## total 0.014 0.008 1.698 0.089semPaths(fit_fat)
###fat and TBS adjusted with log transformed mediators
model_fat_adj_TBS_log <- ' # direct effect
TBSL1L2L3L4_final ~ i*fat + age_final + female_b2 + vitd_top + BMI_b2 + alcohol_freq_8yr + diabetes_bone2 + bone6f_b2
# mediator
log_IL6 ~ a*fat
log_tnf ~ c*fat
log_il1B ~ e*fat
log_crp ~ g*fat
TBSL1L2L3L4_final ~ b*log_IL6
TBSL1L2L3L4_final ~ d*log_tnf
TBSL1L2L3L4_final ~ f*log_il1B
TBSL1L2L3L4_final ~ h*log_crp
# indirect effect (a*b)
ab := a*b
cd := c*d
ef := e*f
# total effect
total := i + (a*b) +(c*d) +(e*f) +(g*h)
'
fit_fat_log <- sem(model_fat_adj_TBS_log, data = db2)
summary(fit_fat_log,fit.measures=TRUE, standardized=TRUE, ci=TRUE)## lavaan 0.6-18 ended normally after 52 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 21
##
## Used Total
## Number of observations 362 445
##
## Model Test User Model:
##
## Test statistic 130.922
## Degrees of freedom 34
## P-value (Chi-square) 0.000
##
## Model Test Baseline Model:
##
## Test statistic 162.003
## Degrees of freedom 50
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.135
## Tucker-Lewis Index (TLI) -0.273
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -1719.623
## Loglikelihood unrestricted model (H1) NA
##
## Akaike (AIC) 3481.246
## Bayesian (BIC) 3562.971
## Sample-size adjusted Bayesian (SABIC) 3496.347
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.089
## 90 Percent confidence interval - lower 0.073
## 90 Percent confidence interval - upper 0.105
## P-value H_0: RMSEA <= 0.050 0.000
## P-value H_0: RMSEA >= 0.080 0.825
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.068
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## TBSL1L2L3L4_final ~
## fat (i) 0.019 0.009 2.062 0.039 0.001 0.037
## age_final -0.000 0.001 -0.289 0.773 -0.003 0.002
## female_b2 -0.020 0.020 -1.020 0.308 -0.058 0.018
## vitd_top -0.002 0.001 -1.206 0.228 -0.004 0.001
## BMI_b2 -0.002 0.001 -1.574 0.116 -0.004 0.000
## alchl_fr_8 0.012 0.015 0.759 0.448 -0.018 0.042
## diabts_bn2 -0.036 0.016 -2.196 0.028 -0.067 -0.004
## bone6f_b2 -0.050 0.024 -2.088 0.037 -0.097 -0.003
## log_IL6 ~
## fat (a) -0.120 0.063 -1.912 0.056 -0.243 0.003
## log_tnf ~
## fat (c) -0.015 0.029 -0.511 0.609 -0.072 0.042
## log_il1B ~
## fat (e) -0.019 0.051 -0.376 0.707 -0.120 0.081
## log_crp ~
## fat (g) -0.049 0.075 -0.654 0.513 -0.195 0.098
## TBSL1L2L3L4_final ~
## log_IL6 (b) 0.010 0.007 1.408 0.159 -0.004 0.024
## log_tnf (d) -0.006 0.015 -0.390 0.697 -0.036 0.024
## log_il1B (f) 0.004 0.009 0.513 0.608 -0.013 0.022
## log_crp (h) -0.012 0.006 -1.997 0.046 -0.024 -0.000
## Std.lv Std.all
##
## 0.019 0.113
## -0.000 -0.015
## -0.020 -0.054
## -0.002 -0.065
## -0.002 -0.084
## 0.012 0.040
## -0.036 -0.114
## -0.050 -0.108
##
## -0.120 -0.100
##
## -0.015 -0.027
##
## -0.019 -0.020
##
## -0.049 -0.034
##
## 0.010 0.072
## -0.006 -0.020
## 0.004 0.026
## -0.012 -0.101
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## .TBSL1L2L3L4_fn 0.022 0.002 13.454 0.000 0.019 0.025
## .log_IL6 1.199 0.089 13.454 0.000 1.024 1.373
## .log_tnf 0.256 0.019 13.454 0.000 0.219 0.293
## .log_il1B 0.798 0.059 13.454 0.000 0.682 0.915
## .log_crp 1.700 0.126 13.454 0.000 1.452 1.947
## Std.lv Std.all
## 0.022 0.931
## 1.199 0.990
## 0.256 0.999
## 0.798 1.000
## 1.700 0.999
##
## Defined Parameters:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## ab -0.001 0.001 -1.134 0.257 -0.003 0.001
## cd 0.000 0.000 0.310 0.757 -0.000 0.001
## ef -0.000 0.000 -0.303 0.762 -0.001 0.000
## total 0.018 0.009 1.991 0.047 0.000 0.037
## Std.lv Std.all
## -0.001 -0.007
## 0.000 0.001
## -0.000 -0.001
## 0.018 0.110semPaths(fit_fat_log)
####Run adjusted models with “estimator = MLM” since 1 of the independent vars (skim) and all mediator vars aren’t normally distributed
model_milk_mlm <- ' # direct effect
BMSi ~ i*milk
# mediator
IL6 ~ a*milk
TNFa ~ c*milk
IL1B ~ e*milk
CRP ~ g*milk
BMSi ~ b*IL6
BMSi ~ d*TNFa
BMSi ~ f*IL1B
BMSi ~ h*CRP
# indirect effect (a*b)
ab := a*b
cd := c*d
ef := e*f
gh := g*h
# total effect
total := i + (a*b) +(c*d) +(e*f) +(g*h)
'
fit_milk_adj_mlm <- sem(model_milk_mlm, data = db, estimator = "MLM")
summary(fit_milk_adj_mlm, fit.measures=TRUE, standardized=TRUE, ci=TRUE)## lavaan 0.6-18 ended normally after 1 iteration
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 14
##
## Used Total
## Number of observations 151 163
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 8.559 8.020
## Degrees of freedom 6 6
## P-value (Chi-square) 0.200 0.237
## Scaling correction factor 1.067
## Satorra-Bentler correction
##
## Model Test Baseline Model:
##
## Test statistic 21.256 22.634
## Degrees of freedom 15 15
## P-value 0.129 0.092
## Scaling correction factor 0.939
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.591 0.735
## Tucker-Lewis Index (TLI) -0.023 0.338
##
## Robust Comparative Fit Index (CFI) 0.699
## Robust Tucker-Lewis Index (TLI) 0.248
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -2694.485 -2694.485
## Loglikelihood unrestricted model (H1) -2690.206 -2690.206
##
## Akaike (AIC) 5416.970 5416.970
## Bayesian (BIC) 5459.212 5459.212
## Sample-size adjusted Bayesian (SABIC) 5414.904 5414.904
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.053 0.047
## 90 Percent confidence interval - lower 0.000 0.000
## 90 Percent confidence interval - upper 0.127 0.120
## P-value H_0: RMSEA <= 0.050 0.405 0.453
## P-value H_0: RMSEA >= 0.080 0.331 0.282
##
## Robust RMSEA 0.049
## 90 Percent confidence interval - lower 0.000
## 90 Percent confidence interval - upper 0.127
## P-value H_0: Robust RMSEA <= 0.050 0.437
## P-value H_0: Robust RMSEA >= 0.080 0.313
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.050 0.050
##
## Parameter Estimates:
##
## Standard errors Robust.sem
## Information Expected
## Information saturated (h1) model Structured
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## BMSi ~
## milk (i) 0.958 0.768 1.248 0.212 -0.547 2.462
## IL6 ~
## milk (a) -0.588 0.262 -2.241 0.025 -1.102 -0.074
## TNFa ~
## milk (c) 0.682 0.818 0.834 0.404 -0.921 2.286
## IL1B ~
## milk (e) -1.824 2.956 -0.617 0.537 -7.618 3.970
## CRP ~
## milk (g) -1.618 0.600 -2.698 0.007 -2.793 -0.442
## BMSi ~
## IL6 (b) -0.120 0.120 -1.007 0.314 -0.355 0.114
## TNFa (d) -0.029 0.073 -0.398 0.691 -0.171 0.113
## IL1B (f) -0.019 0.027 -0.689 0.491 -0.071 0.034
## CRP (h) -0.079 0.086 -0.922 0.357 -0.248 0.089
## Std.lv Std.all
##
## 0.958 0.093
##
## -0.588 -0.100
##
## 0.682 0.075
##
## -1.824 -0.053
##
## -1.618 -0.196
##
## -0.120 -0.068
## -0.029 -0.026
## -0.019 -0.062
## -0.079 -0.063
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## .BMSi 64.811 7.625 8.500 0.000 49.866 79.756
## .IL6 21.222 13.536 1.568 0.117 -5.307 47.751
## .TNFa 52.186 17.860 2.922 0.003 17.181 87.190
## .IL1B 738.733 144.950 5.096 0.000 454.637 1022.829
## .CRP 40.972 11.123 3.683 0.000 19.171 62.774
## Std.lv Std.all
## 64.811 0.974
## 21.222 0.990
## 52.186 0.994
## 738.733 0.997
## 40.972 0.962
##
## Defined Parameters:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## ab 0.071 0.073 0.972 0.331 -0.072 0.213
## cd -0.020 0.049 -0.399 0.690 -0.117 0.077
## ef 0.034 0.059 0.576 0.565 -0.081 0.149
## gh 0.128 0.153 0.838 0.402 -0.172 0.428
## total 1.171 0.747 1.567 0.117 -0.294 2.636
## Std.lv Std.all
## 0.071 0.007
## -0.020 -0.002
## 0.034 0.003
## 0.128 0.012
## 1.171 0.114semPaths(fit_milk_adj_mlm)
fluid adjusted MLM
model_fluid_mlm <- ' # direct effect
BMSi ~ i*fluid + age_final + female_b2 + PA_SCORE_b2 + vitd_top + BMI_b2 + alcohol_freq_8yr +diabetes_bone2 + PTH_8yr
# mediator
IL6 ~ a*fluid
TNFa ~ c*fluid
IL1B ~ e*fluid
CRP ~ g*fluid
BMSi ~ b*IL6
BMSi ~ d*TNFa
BMSi ~ f*IL1B
BMSi ~ h*CRP
# indirect effect (a*b)
ab := a*b
cd := c*d
ef := e*f
gh := g*h
# total effect
total := i + (a*b) +(c*d) +(e*f) +(g*h)
'
fit_fluid_adj_mlm <- sem(model_fluid_mlm, data = db, estimator = "MLM")
summary(fit_fluid_adj_mlm, fit.measures=TRUE, standardized=TRUE, ci=TRUE)## lavaan 0.6-18 ended normally after 1 iteration
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 22
##
## Used Total
## Number of observations 129 163
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 66.706 67.058
## Degrees of freedom 38 38
## P-value (Chi-square) 0.003 0.003
## Scaling correction factor 0.995
## Satorra-Bentler correction
##
## Model Test Baseline Model:
##
## Test statistic 89.288 96.134
## Degrees of freedom 55 55
## P-value 0.002 0.001
## Scaling correction factor 0.929
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.163 0.294
## Tucker-Lewis Index (TLI) -0.212 -0.022
##
## Robust Comparative Fit Index (CFI) 0.243
## Robust Tucker-Lewis Index (TLI) -0.095
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -2310.539 -2310.539
## Loglikelihood unrestricted model (H1) -2277.186 -2277.186
##
## Akaike (AIC) 4665.078 4665.078
## Bayesian (BIC) 4727.994 4727.994
## Sample-size adjusted Bayesian (SABIC) 4658.415 4658.415
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.077 0.077
## 90 Percent confidence interval - lower 0.045 0.045
## 90 Percent confidence interval - upper 0.106 0.107
## P-value H_0: RMSEA <= 0.050 0.079 0.076
## P-value H_0: RMSEA >= 0.080 0.449 0.459
##
## Robust RMSEA 0.077
## 90 Percent confidence interval - lower 0.045
## 90 Percent confidence interval - upper 0.106
## P-value H_0: Robust RMSEA <= 0.050 0.076
## P-value H_0: Robust RMSEA >= 0.080 0.455
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.069 0.069
##
## Parameter Estimates:
##
## Standard errors Robust.sem
## Information Expected
## Information saturated (h1) model Structured
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## BMSi ~
## fluid (i) 1.932 0.766 2.522 0.012 0.430 3.433
## age_final -0.190 0.114 -1.662 0.096 -0.414 0.034
## female_b2 -0.168 1.984 -0.085 0.933 -4.056 3.721
## PA_SCORE_2 0.135 0.127 1.060 0.289 -0.115 0.385
## vitd_top -0.069 0.132 -0.527 0.598 -0.328 0.189
## BMI_b2 -0.287 0.128 -2.237 0.025 -0.539 -0.036
## alchl_fr_8 -0.364 1.499 -0.243 0.808 -3.303 2.575
## diabts_bn2 -0.018 1.396 -0.013 0.989 -2.755 2.718
## PTH_8yr 0.016 0.010 1.532 0.126 -0.004 0.036
## IL6 ~
## fluid (a) -0.463 0.293 -1.579 0.114 -1.038 0.112
## TNFa ~
## fluid (c) 0.416 0.807 0.516 0.606 -1.166 1.998
## IL1B ~
## fluid (e) -3.092 2.400 -1.289 0.198 -7.796 1.611
## CRP ~
## fluid (g) -1.328 0.496 -2.678 0.007 -2.300 -0.356
## BMSi ~
## IL6 (b) -0.168 0.108 -1.555 0.120 -0.379 0.044
## TNFa (d) -0.064 0.064 -1.004 0.316 -0.189 0.061
## IL1B (f) -0.013 0.029 -0.453 0.650 -0.070 0.044
## CRP (h) -0.018 0.090 -0.204 0.838 -0.195 0.158
## Std.lv Std.all
##
## 1.932 0.196
## -0.190 -0.148
## -0.168 -0.009
## 0.135 0.094
## -0.069 -0.048
## -0.287 -0.196
## -0.364 -0.024
## -0.018 -0.001
## 0.016 0.080
##
## -0.463 -0.079
##
## 0.416 0.047
##
## -3.092 -0.096
##
## -1.328 -0.169
##
## -0.168 -0.100
## -0.064 -0.057
## -0.013 -0.043
## -0.018 -0.015
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## .BMSi 60.569 7.849 7.717 0.000 45.185 75.952
## .IL6 24.364 15.613 1.561 0.119 -6.236 54.965
## .TNFa 54.401 20.897 2.603 0.009 13.443 95.359
## .IL1B 724.429 155.183 4.668 0.000 420.277 1028.582
## .CRP 42.703 12.170 3.509 0.000 18.851 66.555
## Std.lv Std.all
## 60.569 0.878
## 24.364 0.994
## 54.401 0.998
## 724.429 0.991
## 42.703 0.972
##
## Defined Parameters:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## ab 0.078 0.060 1.296 0.195 -0.040 0.195
## cd -0.027 0.050 -0.530 0.596 -0.125 0.072
## ef 0.041 0.088 0.465 0.642 -0.132 0.214
## gh 0.024 0.120 0.203 0.839 -0.211 0.260
## total 2.048 0.738 2.774 0.006 0.601 3.495
## Std.lv Std.all
## 0.078 0.008
## -0.027 -0.003
## 0.041 0.004
## 0.024 0.002
## 2.048 0.208semPaths(fit_fluid_adj_mlm)
total adjusted MLM
model_total_mlm <- ' # direct effect
BMSi ~ i*mod + age_final + female_b2 + PA_SCORE_b2 + vitd_top + BMI_b2 + alcohol_freq_8yr + diabetes_bone2 + PTH_8yr
# mediator
IL6 ~ a*mod
TNFa ~ c*mod
IL1B ~ e*mod
CRP ~ g*mod
BMSi ~ b*IL6
BMSi ~ d*TNFa
BMSi ~ f*IL1B
BMSi ~ h*CRP
# indirect effect (a*b)
ab := a*b
cd := c*d
ef := e*f
gh := g*h
# total effect
total := i + (a*b) +(c*d) +(e*f) +(g*h)
'
fit_total_adj_mlm <- sem(model_total_mlm, data = db, estimator="MLM")
summary(fit_total_adj_mlm,fit.measures=TRUE, standardized=TRUE,ci=TRUE)## lavaan 0.6-18 ended normally after 9 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 22
##
## Used Total
## Number of observations 129 163
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 65.626 66.107
## Degrees of freedom 38 38
## P-value (Chi-square) 0.004 0.003
## Scaling correction factor 0.993
## Satorra-Bentler correction
##
## Model Test Baseline Model:
##
## Test statistic 89.166 96.353
## Degrees of freedom 55 55
## P-value 0.002 0.000
## Scaling correction factor 0.925
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.191 0.320
## Tucker-Lewis Index (TLI) -0.170 0.016
##
## Robust Comparative Fit Index (CFI) 0.271
## Robust Tucker-Lewis Index (TLI) -0.055
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -2310.060 -2310.060
## Loglikelihood unrestricted model (H1) -2277.246 -2277.246
##
## Akaike (AIC) 4664.119 4664.119
## Bayesian (BIC) 4727.035 4727.035
## Sample-size adjusted Bayesian (SABIC) 4657.456 4657.456
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.075 0.076
## 90 Percent confidence interval - lower 0.043 0.044
## 90 Percent confidence interval - upper 0.105 0.106
## P-value H_0: RMSEA <= 0.050 0.092 0.087
## P-value H_0: RMSEA >= 0.080 0.418 0.432
##
## Robust RMSEA 0.075
## 90 Percent confidence interval - lower 0.044
## 90 Percent confidence interval - upper 0.105
## P-value H_0: Robust RMSEA <= 0.050 0.088
## P-value H_0: Robust RMSEA >= 0.080 0.426
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.069 0.069
##
## Parameter Estimates:
##
## Standard errors Robust.sem
## Information Expected
## Information saturated (h1) model Structured
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## BMSi ~
## mod (i) 2.087 0.739 2.822 0.005 0.637 3.536
## age_final -0.185 0.112 -1.651 0.099 -0.405 0.035
## female_b2 -0.276 1.993 -0.138 0.890 -4.182 3.630
## PA_SCORE_2 0.120 0.127 0.949 0.343 -0.128 0.369
## vitd_top -0.084 0.134 -0.629 0.529 -0.346 0.178
## BMI_b2 -0.279 0.128 -2.182 0.029 -0.530 -0.028
## alchl_fr_8 -0.301 1.539 -0.196 0.845 -3.318 2.716
## diabts_bn2 -0.018 1.396 -0.013 0.990 -2.754 2.718
## PTH_8yr 0.016 0.010 1.615 0.106 -0.004 0.036
## IL6 ~
## mod (a) -0.372 0.301 -1.235 0.217 -0.963 0.218
## TNFa ~
## mod (c) 0.200 0.821 0.243 0.808 -1.410 1.809
## IL1B ~
## mod (e) -3.292 2.339 -1.407 0.159 -7.877 1.293
## CRP ~
## mod (g) -1.462 0.488 -2.997 0.003 -2.418 -0.506
## BMSi ~
## IL6 (b) -0.174 0.113 -1.530 0.126 -0.396 0.049
## TNFa (d) -0.058 0.066 -0.881 0.378 -0.186 0.071
## IL1B (f) -0.012 0.029 -0.411 0.681 -0.069 0.045
## CRP (h) -0.018 0.090 -0.198 0.843 -0.194 0.158
## Std.lv Std.all
##
## 2.087 0.210
## -0.185 -0.144
## -0.276 -0.015
## 0.120 0.084
## -0.084 -0.058
## -0.279 -0.191
## -0.301 -0.020
## -0.018 -0.001
## 0.016 0.085
##
## -0.372 -0.063
##
## 0.200 0.023
##
## -3.292 -0.102
##
## -1.462 -0.184
##
## -0.174 -0.103
## -0.058 -0.051
## -0.012 -0.039
## -0.018 -0.014
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## .BMSi 60.286 7.713 7.816 0.000 45.169 75.404
## .IL6 24.420 15.631 1.562 0.118 -6.216 55.055
## .TNFa 54.495 20.930 2.604 0.009 13.473 95.518
## .IL1B 723.643 153.841 4.704 0.000 422.120 1025.167
## .CRP 42.460 12.097 3.510 0.000 18.751 66.170
## Std.lv Std.all
## 60.286 0.874
## 24.420 0.996
## 54.495 0.999
## 723.643 0.990
## 42.460 0.966
##
## Defined Parameters:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## ab 0.065 0.050 1.298 0.194 -0.033 0.162
## cd -0.012 0.046 -0.250 0.803 -0.102 0.079
## ef 0.039 0.093 0.422 0.673 -0.144 0.223
## gh 0.026 0.131 0.198 0.843 -0.232 0.284
## total 2.205 0.720 3.064 0.002 0.794 3.616
## Std.lv Std.all
## 0.065 0.006
## -0.012 -0.001
## 0.039 0.004
## 0.026 0.003
## 2.205 0.222semPaths(fit_total_adj_mlm)
skim adj MLM
model_skim_TBS_mlm <- ' # direct effect
TBSL1L2L3L4_final ~ i*skim + age_final + female_b2 + vitd_top + BMI_b2 + alcohol_freq_8yr + diabetes_bone2 + bone6f_b2
# mediator
IL6 ~ a*skim
TNFa ~ c*skim
IL1B ~ e*skim
CRP ~ g*skim
TBSL1L2L3L4_final ~ b*IL6
TBSL1L2L3L4_final ~ d*TNFa
TBSL1L2L3L4_final ~ f*IL1B
TBSL1L2L3L4_final ~ h*CRP
# indirect effect (a*b)
ab := a*b
cd := c*d
ef := e*f
gh :=g*h
# total effect
total := i + (a*b) +(c*d) +(e*f) +(g*h)
'
fit_skim_adj_mlm <- sem(model_skim_TBS_mlm, data = db2, estimator="MLM")## Warning: lavaan->lav_data_full():
## some observed variances are (at least) a factor 1000 times larger than
## others; use varTable(fit) to investigatesummary(fit_skim_adj_mlm,fit.measures=TRUE, standardized=TRUE,ci=TRUE)## lavaan 0.6-18 ended normally after 78 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 21
##
## Used Total
## Number of observations 362 445
##
## Model Test User Model:
## Standard Scaled
## Test Statistic 116.466 80.616
## Degrees of freedom 34 34
## P-value (Chi-square) 0.000 0.000
## Scaling correction factor 1.445
## Satorra-Bentler correction
##
## Model Test Baseline Model:
##
## Test statistic 143.150 112.719
## Degrees of freedom 50 50
## P-value 0.000 0.000
## Scaling correction factor 1.270
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.115 0.257
## Tucker-Lewis Index (TLI) -0.302 -0.093
##
## Robust Comparative Fit Index (CFI) 0.154
## Robust Tucker-Lewis Index (TLI) -0.243
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -5447.407 -5447.407
## Loglikelihood unrestricted model (H1) NA NA
##
## Akaike (AIC) 10936.813 10936.813
## Bayesian (BIC) 11018.538 11018.538
## Sample-size adjusted Bayesian (SABIC) 10951.914 10951.914
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.082 0.062
## 90 Percent confidence interval - lower 0.066 0.047
## 90 Percent confidence interval - upper 0.098 0.076
## P-value H_0: RMSEA <= 0.050 0.001 0.090
## P-value H_0: RMSEA >= 0.080 0.593 0.017
##
## Robust RMSEA 0.074
## 90 Percent confidence interval - lower 0.053
## 90 Percent confidence interval - upper 0.095
## P-value H_0: Robust RMSEA <= 0.050 0.030
## P-value H_0: Robust RMSEA >= 0.080 0.336
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.061 0.061
##
## Parameter Estimates:
##
## Standard errors Robust.sem
## Information Expected
## Information saturated (h1) model Structured
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## TBSL1L2L3L4_final ~
## skim (i) -0.039 0.027 -1.434 0.151 -0.092 0.014
## age_final -0.000 0.001 -0.102 0.919 -0.002 0.002
## female_b2 -0.015 0.018 -0.816 0.414 -0.051 0.021
## vitd_top -0.001 0.001 -0.478 0.633 -0.003 0.002
## BMI_b2 -0.002 0.001 -1.704 0.088 -0.005 0.000
## alchl_fr_8 0.001 0.014 0.090 0.928 -0.026 0.029
## diabts_bn2 -0.033 0.015 -2.161 0.031 -0.063 -0.003
## bone6f_b2 -0.056 0.024 -2.372 0.018 -0.102 -0.010
## IL6 ~
## skim (a) 0.637 0.870 0.732 0.464 -1.069 2.343
## TNFa ~
## skim (c) 0.328 0.606 0.541 0.589 -0.860 1.515
## IL1B ~
## skim (e) 1.156 4.323 0.267 0.789 -7.318 9.629
## CRP ~
## skim (g) -1.888 0.866 -2.181 0.029 -3.585 -0.191
## TBSL1L2L3L4_final ~
## IL6 (b) 0.000 0.001 0.180 0.857 -0.002 0.003
## TNFa (d) -0.000 0.001 -0.230 0.818 -0.002 0.002
## IL1B (f) 0.000 0.000 1.515 0.130 -0.000 0.001
## CRP (h) -0.000 0.001 -0.251 0.802 -0.001 0.001
## Std.lv Std.all
##
## -0.039 -0.108
## -0.000 -0.005
## -0.015 -0.041
## -0.001 -0.026
## -0.002 -0.105
## 0.001 0.004
## -0.033 -0.105
## -0.056 -0.121
##
## 0.637 0.045
##
## 0.328 0.019
##
## 1.156 0.013
##
## -1.888 -0.070
##
## 0.000 0.008
## -0.000 -0.010
## 0.000 0.055
## -0.000 -0.010
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## .TBSL1L2L3L4_fn 0.022 0.003 8.054 0.000 0.017 0.028
## .IL6 35.996 9.652 3.729 0.000 17.078 54.914
## .TNFa 55.346 16.624 3.329 0.001 22.763 87.929
## .IL1B 1390.927 288.394 4.823 0.000 825.685 1956.169
## .CRP 131.141 55.924 2.345 0.019 21.531 240.751
## Std.lv Std.all
## 0.022 0.938
## 35.996 0.998
## 55.346 1.000
## 1390.927 1.000
## 131.141 0.995
##
## Defined Parameters:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## ab 0.000 0.001 0.181 0.856 -0.001 0.002
## cd -0.000 0.000 -0.203 0.839 -0.001 0.001
## ef 0.000 0.001 0.260 0.795 -0.002 0.002
## gh 0.000 0.001 0.258 0.796 -0.002 0.002
## total -0.038 0.027 -1.426 0.154 -0.091 0.014
## Std.lv Std.all
## 0.000 0.000
## -0.000 -0.000
## 0.000 0.001
## 0.000 0.001
## -0.038 -0.106semPaths(fit_skim_adj_mlm)