Objective
Modelling progression of the dengue illness phenotype. Replication of the SEM analysis presented in:
Park, S., Srikiatkhachorn, A., Kalayanarooj, S., Macareo, L., Green, S., Friedman, J. F., & Rothman, A. L. (2018). Use of structural equation models to predict dengue illness phenotype. PLoS Neglected Tropical Diseases, 12(10), 1–14. https://doi.org/10.1371/journal.pntd.0006799
The paper was worried about the evolution of the Dengue virus (DENV) infection, which, in severe cases, leads to Dengue Haemorrhagic Fever (DHF), characterized by fever, plasma leakage, bleeding diathesis, and thrombocytopenia. Platelet counts and hepatic parameters like ALT were monitored in three moments of time to model the progression of the phenotype in dengue illness.
Original method: SEM using Mplus 8 statistical software. SEM parameters were estimated using the weighted least squares means and variances adjusted estimator with the theta parameterization
Method applied in this analysis: CB-SEM with MLR estimator in R’s
package Lavaan. For simplicity, we are not discussing weighted models
yet in this post. So, note this is not an exact replication. We are
taking a lot of freedom in adjusting models and analysis here.
Data acquisition
library(openxlsx)
## Warning: package 'openxlsx' was built under R version 4.1.3
data<-read.xlsx("Park2018.xlsx")
Let’s explore the datastructure.
str(data)
## 'data.frame': 257 obs. of 22 variables:
## $ age2 : chr "12-13" "4-5" "4-5" "8-9" ...
## $ sex : num 1 1 2 2 1 1 1 1 2 2 ...
## $ dengue : num 1 1 0 1 1 0 1 1 1 1 ...
## $ dhf : num 1 0 0 0 0 0 0 0 0 0 ...
## $ dhf34 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ ast_m3 : num 25 38 27 167 29 39 32 48 36 35 ...
## $ alt_m3 : num 10 14 9 109 13 15 10 23 18 16 ...
## $ wbc_m3 : num 3600 7200 9200 2200 9500 8000 5200 5000 2800 6000 ...
## $ lymph_m3 : num 16 21 13 34 7 21 16 18 37 11 ...
## $ albumin_m3 : num 4.5 5.6 4.6 4.8 5 5.9 4.6 3.9 4 4.2 ...
## $ max_hct_m3 : num 42.5 38 37 40 38 40 42.5 39 38 40 ...
## $ platelets_m3: num 271000 272000 216000 227000 204000 287000 266000 307000 206000 273000 ...
## $ tourn_no_m3 : num 21 21 10 21 5 8 21 4 6 4 ...
## $ ast_m1 : num 53 36 26 248 34 35 43 43 240 97 ...
## $ alt_m1 : num 15 14 11 174 14 11 9 24 126 28 ...
## $ wbc_m1 : num 2300 5100 3800 1600 6500 7300 2800 3800 600 3300 ...
## $ lymph_m1 : num 32 60 41 39 61 45 24 35 42 32 ...
## $ albumin_m1 : num 4.3 4.6 3.7 4.5 4.9 4.9 3.9 3.8 4.4 4.5 ...
## $ max_hct_m1 : num 43 39 37 40 36 37 41 39 38 45 ...
## $ platelets_m1: num 73000 263000 200000 116000 163000 262000 168000 147000 180000 106000 ...
## $ tourn_no_m1 : num 21 21 0 21 2 4 21 20 14 21 ...
## $ age_t : num 12 4 4 8 6 4 8 8 4 6 ...
In this dataset, outcomes cannot be described by a single parameter, but by a set of complementary and possibly multicollinear parameters. Note also that the parameters are monitored and assessed multiple times over a specific period, as the time for results to become apparent can also vary. Such sequential measures are certainly associated. Notably, the intervention improves or worsens, but the ultimate level of results depends on the initial measure.
The same parameters (like platelet count and ALT levels) are assessed 3 days and 1 day before the event (indicated with m3 and m1 at the end of the variable name).
Model
So, the model reflect such association:
-
causal relation among DHF (dengue hemorrhagic fever) and measures 1 day before the event
-
the measures at 1 day before the event as potentially influenced by all the measures at 3 days before the event.
-
hypotheses about the influence of age in the outcome, but also on measures at m3
-
and consider also that the measures can be correlated each other (for example, ALT and AST are known enzymes associated with hepatotoxicity, for example.
library(lavaan)
model="
dhf~alt_m1+lymph_m1+max_hct_m1+platelets_m1
ast_m1~alt_m3+wbc_m3+lymph_m3+albumin_m3+platelets_m3+age_t+ast_m3
alt_m1~alt_m3+wbc_m3+lymph_m3+albumin_m3+platelets_m3+ast_m3
wbc_m1~ast_m3+alt_m3+wbc_m3+lymph_m3+albumin_m3+age_t
lymph_m1~wbc_m3+lymph_m3+max_hct_m3+age_t
albumin_m1~ast_m3+alt_m3+albumin_m3+platelets_m3
max_hct_m1~wbc_m3+lymph_m3+albumin_m3+max_hct_m3+age_t
platelets_m1~wbc_m3+lymph_m3+platelets_m3
tourn_no_m1~ast_m3+wbc_m3+lymph_m3+albumin_m3+tourn_no_m3+age_t
alt_m3~age_t
wbc_m3~age_t
lymph_m3~age_t
max_hct_m3~age_t
platelets_m3~age_t
tourn_no_m3~age_t
# covariances
ast_m1~~alt_m1+albumin_m1+max_hct_m1
alt_m1~~albumin_m1+max_hct_m1
wbc_m1~~lymph_m1+platelets_m1
lymph_m1~~tourn_no_m1
albumin_m1~~platelets_m1
max_hct_m1~~platelets_m1+tourn_no_m1
platelets_m1~~tourn_no_m1
ast_m3~~wbc_m3+platelets_m3
alt_m3~~wbc_m3+platelets_m3+ast_m3
wbc_m3~~lymph_m3+platelets_m3+tourn_no_m3
lymph_m3~~platelets_m3+tourn_no_m3
max_hct_m3~~platelets_m3
"
fit=sem(model=model, data=data,std.ov=TRUE,estimator="MLR",fixed.x = FALSE)
Visualization
Visualization was generated using R’s package semPlots, with some
adjustment of the coordinates for each of the variables, and also adding
p values for paths.
#17 nodes
ly<-matrix(NA,18,2)
depVar='dhf'
med1=c('ast_m1','alt_m1','wbc_m1','lymph_m1','albumin_m1','max_hct_m1','platelets_m1','tourn_no_m1')
med2=c('ast_m3','alt_m3','wbc_m3','lymph_m3','albumin_m3','max_hct_m3','platelets_m3','tourn_no_m3')
indepVar='age_t'
labels=c()
labels[1]=depVar
ly[1,]=c(1,0)
y=1
for (x in c(1:length(med1))){
ly[y+x,]=c(0.6,(x/8*1.6-1))
labels[(x+y)]<-med1[x]
}
y=9
for (x in c(1:length(med2))){
ly[y+x,]=c(-1,(x/8*1.6-1))
labels[(x+y)]<-med2[x]
}
labels[18]=indepVar
ly[18,]=c(-0.5,1)
table2<-parameterEstimates(fit,standardized=TRUE)%>%as.data.frame()
table2<-table2[!table2$lhs==table2$rhs,]
b<-gettextf('%.3f \n p=%.3f', table2$std.all, digits=table2$pvalue)
semPaths(fit, layout=ly,
edgeLabels=b,
residuals=FALSE,
style='ram',
what='est',
whatLabels = "std",
cut=0.3,
sizeMan = 10, # Size of manifest variables
sizeMan2=3,edge.label.cex = 0.8,label.cex=1,
nCharNodes = 0,fade=TRUE,
mar = c(1,3,1,3))
Attend how the association among the sequential measures of the variables (m1 and m3) is fragrant. Also note the different parameters are associated. For example, the AST levels on day 3 are significantly associated with albumin levels on day 1.
Parameter table
The summarization on fit measures and parameter estimates are presented bellow. The model is an almost saturated model, and can be still adjusted by removing non-significant paths, for example. Almost because using logic/theory we have not allowed the age being an independent variable for outcome (dhf). But we let it influencing not just the initial measures (at -3 days), but also the measure 1 day before the event. But the results show the model fits well, and that path is not required.
The further adjustment is required/indicated to increase degrees of freedom. With such adjustments, possibly we will depict better some paths which currently standard errors are so high to distinguish if it is significant or not.
summary(fit, fit.measures=TRUE)
## lavaan 0.6-11 ended normally after 48 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 102
##
## Number of observations 257
##
## Model Test User Model:
## Standard Robust
## Test Statistic 99.387 91.350
## Degrees of freedom 69 69
## P-value (Chi-square) 0.010 0.037
## Scaling correction factor 1.088
## Yuan-Bentler correction (Mplus variant)
##
## Model Test Baseline Model:
##
## Test statistic 2032.225 1299.643
## Degrees of freedom 152 152
## P-value 0.000 0.000
## Scaling correction factor 1.564
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.984 0.981
## Tucker-Lewis Index (TLI) 0.964 0.957
##
## Robust Comparative Fit Index (CFI) 0.986
## Robust Tucker-Lewis Index (TLI) 0.970
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -5587.968 -5587.968
## Scaling correction factor 2.743
## for the MLR correction
## Loglikelihood unrestricted model (H1) -5538.274 -5538.274
## Scaling correction factor 2.075
## for the MLR correction
##
## Akaike (AIC) 11379.935 11379.935
## Bayesian (BIC) 11741.941 11741.941
## Sample-size adjusted Bayesian (BIC) 11418.570 11418.570
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.041 0.036
## 90 Percent confidence interval - lower 0.021 0.011
## 90 Percent confidence interval - upper 0.059 0.053
## P-value RMSEA <= 0.05 0.779 0.908
##
## Robust RMSEA 0.037
## 90 Percent confidence interval - lower 0.010
## 90 Percent confidence interval - upper 0.056
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.054 0.054
##
## Parameter Estimates:
##
## Standard errors Sandwich
## Information bread Observed
## Observed information based on Hessian
##
## Regressions:
## Estimate Std.Err z-value P(>|z|)
## dhf ~
## alt_m1 0.160 0.059 2.704 0.007
## lymph_m1 -0.107 0.053 -2.004 0.045
## max_hct_m1 0.197 0.057 3.449 0.001
## platelets_m1 -0.243 0.054 -4.461 0.000
## ast_m1 ~
## alt_m3 -0.250 0.057 -4.380 0.000
## wbc_m3 -0.056 0.035 -1.633 0.102
## lymph_m3 -0.161 0.051 -3.154 0.002
## albumin_m3 -0.042 0.025 -1.668 0.095
## platelets_m3 -0.137 0.058 -2.358 0.018
## age_t -0.073 0.071 -1.037 0.300
## ast_m3 0.749 0.105 7.138 0.000
## alt_m1 ~
## alt_m3 0.271 0.155 1.751 0.080
## wbc_m3 -0.071 0.039 -1.845 0.065
## lymph_m3 -0.093 0.031 -3.012 0.003
## albumin_m3 -0.068 0.038 -1.784 0.074
## platelets_m3 -0.093 0.035 -2.699 0.007
## ast_m3 0.445 0.084 5.304 0.000
## wbc_m1 ~
## ast_m3 0.223 0.062 3.595 0.000
## alt_m3 -0.100 0.040 -2.522 0.012
## wbc_m3 0.807 0.056 14.528 0.000
## lymph_m3 0.129 0.040 3.205 0.001
## albumin_m3 -0.104 0.041 -2.522 0.012
## age_t -0.054 0.040 -1.344 0.179
## lymph_m1 ~
## wbc_m3 -0.199 0.049 -4.045 0.000
## lymph_m3 0.281 0.069 4.053 0.000
## max_hct_m3 -0.079 0.054 -1.466 0.143
## age_t -0.175 0.062 -2.818 0.005
## albumin_m1 ~
## ast_m3 -0.108 0.059 -1.829 0.067
## alt_m3 0.008 0.043 0.185 0.853
## albumin_m3 0.501 0.054 9.339 0.000
## platelets_m3 0.104 0.054 1.921 0.055
## max_hct_m1 ~
## wbc_m3 -0.106 0.051 -2.099 0.036
## lymph_m3 -0.147 0.050 -2.918 0.004
## albumin_m3 -0.071 0.047 -1.524 0.128
## max_hct_m3 0.498 0.072 6.960 0.000
## age_t 0.178 0.056 3.180 0.001
## platelets_m1 ~
## wbc_m3 0.312 0.073 4.274 0.000
## lymph_m3 0.085 0.049 1.709 0.087
## platelets_m3 0.519 0.057 9.083 0.000
## tourn_no_m1 ~
## ast_m3 0.125 0.037 3.406 0.001
## wbc_m3 -0.132 0.048 -2.787 0.005
## lymph_m3 -0.136 0.061 -2.239 0.025
## albumin_m3 -0.074 0.049 -1.514 0.130
## tourn_no_m3 0.464 0.052 8.916 0.000
## age_t 0.114 0.055 2.077 0.038
## alt_m3 ~
## age_t 0.127 0.040 3.135 0.002
## wbc_m3 ~
## age_t -0.192 0.051 -3.721 0.000
## lymph_m3 ~
## age_t -0.345 0.061 -5.639 0.000
## max_hct_m3 ~
## age_t 0.341 0.061 5.618 0.000
## platelets_m3 ~
## age_t -0.280 0.061 -4.619 0.000
## tourn_no_m3 ~
## age_t 0.116 0.062 1.866 0.062
##
## Covariances:
## Estimate Std.Err z-value P(>|z|)
## .ast_m1 ~~
## .alt_m1 0.365 0.190 1.924 0.054
## .albumin_m1 0.118 0.107 1.098 0.272
## .max_hct_m1 -0.063 0.035 -1.795 0.073
## .alt_m1 ~~
## .albumin_m1 0.094 0.053 1.764 0.078
## .max_hct_m1 -0.036 0.027 -1.328 0.184
## .wbc_m1 ~~
## .lymph_m1 -0.108 0.036 -2.957 0.003
## .platelets_m1 0.115 0.025 4.607 0.000
## .lymph_m1 ~~
## .tourn_no_m1 -0.113 0.041 -2.730 0.006
## .albumin_m1 ~~
## .platelets_m1 0.157 0.037 4.194 0.000
## .max_hct_m1 ~~
## .platelets_m1 -0.111 0.039 -2.871 0.004
## .tourn_no_m1 0.108 0.041 2.626 0.009
## .platelets_m1 ~~
## .tourn_no_m1 -0.056 0.037 -1.530 0.126
## .wbc_m3 ~~
## ast_m3 -0.162 0.035 -4.688 0.000
## .platelets_m3 ~~
## ast_m3 -0.184 0.092 -1.996 0.046
## .alt_m3 ~~
## .wbc_m3 -0.118 0.033 -3.559 0.000
## .platelets_m3 -0.095 0.054 -1.784 0.074
## ast_m3 0.743 0.274 2.710 0.007
## .wbc_m3 ~~
## .lymph_m3 -0.379 0.051 -7.499 0.000
## .platelets_m3 0.299 0.058 5.130 0.000
## .tourn_no_m3 -0.178 0.053 -3.366 0.001
## .lymph_m3 ~~
## .platelets_m3 -0.153 0.061 -2.530 0.011
## .tourn_no_m3 0.137 0.057 2.403 0.016
## .max_hct_m3 ~~
## .platelets_m3 -0.078 0.055 -1.424 0.154
## .dhf ~~
## .ast_m1 0.017 0.023 0.746 0.456
## .wbc_m1 0.019 0.027 0.691 0.490
## .albumin_m1 -0.018 0.045 -0.404 0.686
## .tourn_no_m1 0.054 0.041 1.311 0.190
## .ast_m1 ~~
## .wbc_m1 -0.010 0.016 -0.604 0.546
## .tourn_no_m1 0.001 0.016 0.075 0.940
## .wbc_m1 ~~
## .albumin_m1 0.022 0.033 0.662 0.508
## .tourn_no_m1 -0.019 0.027 -0.719 0.472
## .albumin_m1 ~~
## .tourn_no_m1 -0.026 0.038 -0.666 0.506
## albumin_m3 ~~
## age_t 0.068 0.060 1.136 0.256
##
## Variances:
## Estimate Std.Err z-value P(>|z|)
## .dhf 0.804 0.078 10.305 0.000
## .ast_m1 0.571 0.394 1.449 0.147
## .alt_m1 0.462 0.146 3.153 0.002
## .wbc_m1 0.382 0.044 8.675 0.000
## .lymph_m1 0.768 0.079 9.739 0.000
## .albumin_m1 0.689 0.087 7.956 0.000
## .max_hct_m1 0.587 0.079 7.412 0.000
## .platelets_m1 0.500 0.045 11.006 0.000
## .tourn_no_m1 0.647 0.053 12.104 0.000
## .alt_m3 0.987 0.408 2.417 0.016
## .wbc_m3 0.943 0.244 3.869 0.000
## .lymph_m3 0.877 0.083 10.608 0.000
## .max_hct_m3 0.880 0.099 8.869 0.000
## .platelets_m3 0.914 0.090 10.187 0.000
## .tourn_no_m3 0.983 0.060 16.407 0.000
## ast_m3 0.996 0.428 2.329 0.020
## albumin_m3 0.996 0.102 9.727 0.000
## age_t 0.996 0.068 14.642 0.000
The fit measures can be also extracted using:
fitmeasures(fit)
## npar fmin
## 102.000 0.193
## chisq df
## 99.387 69.000
## pvalue chisq.scaled
## 0.010 91.350
## df.scaled pvalue.scaled
## 69.000 0.037
## chisq.scaling.factor baseline.chisq
## 1.088 2032.225
## baseline.df baseline.pvalue
## 152.000 0.000
## baseline.chisq.scaled baseline.df.scaled
## 1299.643 152.000
## baseline.pvalue.scaled baseline.chisq.scaling.factor
## 0.000 1.564
## cfi tli
## 0.984 0.964
## nnfi rfi
## 0.964 0.892
## nfi pnfi
## 0.951 0.432
## ifi rni
## 0.985 0.984
## cfi.scaled tli.scaled
## 0.981 0.957
## cfi.robust tli.robust
## 0.986 0.970
## nnfi.scaled nnfi.robust
## 0.957 0.970
## rfi.scaled nfi.scaled
## 0.845 0.930
## ifi.scaled rni.scaled
## 0.982 0.981
## rni.robust logl
## 0.986 -5587.968
## unrestricted.logl aic
## -5538.274 11379.935
## bic ntotal
## 11741.941 257.000
## bic2 scaling.factor.h1
## 11418.570 2.075
## scaling.factor.h0 rmsea
## 2.743 0.041
## rmsea.ci.lower rmsea.ci.upper
## 0.021 0.059
## rmsea.pvalue rmsea.scaled
## 0.779 0.036
## rmsea.ci.lower.scaled rmsea.ci.upper.scaled
## 0.011 0.053
## rmsea.pvalue.scaled rmsea.robust
## 0.908 0.037
## rmsea.ci.lower.robust rmsea.ci.upper.robust
## 0.010 0.056
## rmsea.pvalue.robust rmr
## NA 0.054
## rmr_nomean srmr
## 0.054 0.054
## srmr_bentler srmr_bentler_nomean
## 0.054 0.054
## crmr crmr_nomean
## 0.056 0.056
## srmr_mplus srmr_mplus_nomean
## 0.054 0.054
## cn_05 cn_01
## 232.152 257.587
## gfi agfi
## 0.961 0.903
## pgfi mfi
## 0.388 0.943
## ecvi
## 1.180
And parameter estimates can also obtained by:
parameterestimates(fit,standardized = TRUE)
## lhs op rhs est se z pvalue ci.lower ci.upper
## 1 dhf ~ alt_m1 0.160 0.059 2.704 0.007 0.044 0.276
## 2 dhf ~ lymph_m1 -0.107 0.053 -2.004 0.045 -0.211 -0.002
## 3 dhf ~ max_hct_m1 0.197 0.057 3.449 0.001 0.085 0.309
## 4 dhf ~ platelets_m1 -0.243 0.054 -4.461 0.000 -0.350 -0.136
## 5 ast_m1 ~ alt_m3 -0.250 0.057 -4.380 0.000 -0.362 -0.138
## 6 ast_m1 ~ wbc_m3 -0.056 0.035 -1.633 0.102 -0.124 0.011
## 7 ast_m1 ~ lymph_m3 -0.161 0.051 -3.154 0.002 -0.262 -0.061
## 8 ast_m1 ~ albumin_m3 -0.042 0.025 -1.668 0.095 -0.091 0.007
## 9 ast_m1 ~ platelets_m3 -0.137 0.058 -2.358 0.018 -0.250 -0.023
## 10 ast_m1 ~ age_t -0.073 0.071 -1.037 0.300 -0.212 0.065
## 11 ast_m1 ~ ast_m3 0.749 0.105 7.138 0.000 0.543 0.955
## 12 alt_m1 ~ alt_m3 0.271 0.155 1.751 0.080 -0.032 0.575
## 13 alt_m1 ~ wbc_m3 -0.071 0.039 -1.845 0.065 -0.147 0.004
## 14 alt_m1 ~ lymph_m3 -0.093 0.031 -3.012 0.003 -0.153 -0.032
## 15 alt_m1 ~ albumin_m3 -0.068 0.038 -1.784 0.074 -0.142 0.007
## 16 alt_m1 ~ platelets_m3 -0.093 0.035 -2.699 0.007 -0.161 -0.026
## 17 alt_m1 ~ ast_m3 0.445 0.084 5.304 0.000 0.280 0.609
## 18 wbc_m1 ~ ast_m3 0.223 0.062 3.595 0.000 0.101 0.345
## 19 wbc_m1 ~ alt_m3 -0.100 0.040 -2.522 0.012 -0.178 -0.022
## 20 wbc_m1 ~ wbc_m3 0.807 0.056 14.528 0.000 0.698 0.916
## 21 wbc_m1 ~ lymph_m3 0.129 0.040 3.205 0.001 0.050 0.208
## 22 wbc_m1 ~ albumin_m3 -0.104 0.041 -2.522 0.012 -0.185 -0.023
## 23 wbc_m1 ~ age_t -0.054 0.040 -1.344 0.179 -0.134 0.025
## 24 lymph_m1 ~ wbc_m3 -0.199 0.049 -4.045 0.000 -0.296 -0.103
## 25 lymph_m1 ~ lymph_m3 0.281 0.069 4.053 0.000 0.145 0.416
## 26 lymph_m1 ~ max_hct_m3 -0.079 0.054 -1.466 0.143 -0.186 0.027
## 27 lymph_m1 ~ age_t -0.175 0.062 -2.818 0.005 -0.297 -0.053
## 28 albumin_m1 ~ ast_m3 -0.108 0.059 -1.829 0.067 -0.225 0.008
## 29 albumin_m1 ~ alt_m3 0.008 0.043 0.185 0.853 -0.076 0.092
## 30 albumin_m1 ~ albumin_m3 0.501 0.054 9.339 0.000 0.396 0.606
## 31 albumin_m1 ~ platelets_m3 0.104 0.054 1.921 0.055 -0.002 0.211
## 32 max_hct_m1 ~ wbc_m3 -0.106 0.051 -2.099 0.036 -0.205 -0.007
## 33 max_hct_m1 ~ lymph_m3 -0.147 0.050 -2.918 0.004 -0.245 -0.048
## 34 max_hct_m1 ~ albumin_m3 -0.071 0.047 -1.524 0.128 -0.163 0.020
## 35 max_hct_m1 ~ max_hct_m3 0.498 0.072 6.960 0.000 0.358 0.638
## 36 max_hct_m1 ~ age_t 0.178 0.056 3.180 0.001 0.068 0.288
## 37 platelets_m1 ~ wbc_m3 0.312 0.073 4.274 0.000 0.169 0.455
## 38 platelets_m1 ~ lymph_m3 0.085 0.049 1.709 0.087 -0.012 0.181
## 39 platelets_m1 ~ platelets_m3 0.519 0.057 9.083 0.000 0.407 0.631
## 40 tourn_no_m1 ~ ast_m3 0.125 0.037 3.406 0.001 0.053 0.196
## 41 tourn_no_m1 ~ wbc_m3 -0.132 0.048 -2.787 0.005 -0.226 -0.039
## 42 tourn_no_m1 ~ lymph_m3 -0.136 0.061 -2.239 0.025 -0.254 -0.017
## 43 tourn_no_m1 ~ albumin_m3 -0.074 0.049 -1.514 0.130 -0.170 0.022
## 44 tourn_no_m1 ~ tourn_no_m3 0.464 0.052 8.916 0.000 0.362 0.566
## 45 tourn_no_m1 ~ age_t 0.114 0.055 2.077 0.038 0.006 0.222
## 46 alt_m3 ~ age_t 0.127 0.040 3.135 0.002 0.048 0.206
## 47 wbc_m3 ~ age_t -0.192 0.051 -3.721 0.000 -0.293 -0.091
## 48 lymph_m3 ~ age_t -0.345 0.061 -5.639 0.000 -0.464 -0.225
## 49 max_hct_m3 ~ age_t 0.341 0.061 5.618 0.000 0.222 0.460
## 50 platelets_m3 ~ age_t -0.280 0.061 -4.619 0.000 -0.399 -0.161
## 51 tourn_no_m3 ~ age_t 0.116 0.062 1.866 0.062 -0.006 0.237
## 52 ast_m1 ~~ alt_m1 0.365 0.190 1.924 0.054 -0.007 0.737
## 53 ast_m1 ~~ albumin_m1 0.118 0.107 1.098 0.272 -0.092 0.328
## 54 ast_m1 ~~ max_hct_m1 -0.063 0.035 -1.795 0.073 -0.131 0.006
## 55 alt_m1 ~~ albumin_m1 0.094 0.053 1.764 0.078 -0.010 0.198
## 56 alt_m1 ~~ max_hct_m1 -0.036 0.027 -1.328 0.184 -0.088 0.017
## 57 wbc_m1 ~~ lymph_m1 -0.108 0.036 -2.957 0.003 -0.179 -0.036
## 58 wbc_m1 ~~ platelets_m1 0.115 0.025 4.607 0.000 0.066 0.164
## 59 lymph_m1 ~~ tourn_no_m1 -0.113 0.041 -2.730 0.006 -0.194 -0.032
## 60 albumin_m1 ~~ platelets_m1 0.157 0.037 4.194 0.000 0.083 0.230
## 61 max_hct_m1 ~~ platelets_m1 -0.111 0.039 -2.871 0.004 -0.187 -0.035
## 62 max_hct_m1 ~~ tourn_no_m1 0.108 0.041 2.626 0.009 0.027 0.188
## 63 platelets_m1 ~~ tourn_no_m1 -0.056 0.037 -1.530 0.126 -0.129 0.016
## 64 wbc_m3 ~~ ast_m3 -0.162 0.035 -4.688 0.000 -0.230 -0.094
## 65 platelets_m3 ~~ ast_m3 -0.184 0.092 -1.996 0.046 -0.365 -0.003
## 66 alt_m3 ~~ wbc_m3 -0.118 0.033 -3.559 0.000 -0.183 -0.053
## 67 alt_m3 ~~ platelets_m3 -0.095 0.054 -1.784 0.074 -0.200 0.009
## 68 alt_m3 ~~ ast_m3 0.743 0.274 2.710 0.007 0.206 1.281
## 69 wbc_m3 ~~ lymph_m3 -0.379 0.051 -7.499 0.000 -0.479 -0.280
## 70 wbc_m3 ~~ platelets_m3 0.299 0.058 5.130 0.000 0.185 0.414
## 71 wbc_m3 ~~ tourn_no_m3 -0.178 0.053 -3.366 0.001 -0.281 -0.074
## 72 lymph_m3 ~~ platelets_m3 -0.153 0.061 -2.530 0.011 -0.272 -0.035
## 73 lymph_m3 ~~ tourn_no_m3 0.137 0.057 2.403 0.016 0.025 0.249
## 74 max_hct_m3 ~~ platelets_m3 -0.078 0.055 -1.424 0.154 -0.186 0.029
## 75 dhf ~~ dhf 0.804 0.078 10.305 0.000 0.651 0.957
## 76 ast_m1 ~~ ast_m1 0.571 0.394 1.449 0.147 -0.201 1.343
## 77 alt_m1 ~~ alt_m1 0.462 0.146 3.153 0.002 0.175 0.749
## 78 wbc_m1 ~~ wbc_m1 0.382 0.044 8.675 0.000 0.295 0.468
## 79 lymph_m1 ~~ lymph_m1 0.768 0.079 9.739 0.000 0.613 0.922
## 80 albumin_m1 ~~ albumin_m1 0.689 0.087 7.956 0.000 0.519 0.859
## 81 max_hct_m1 ~~ max_hct_m1 0.587 0.079 7.412 0.000 0.432 0.742
## 82 platelets_m1 ~~ platelets_m1 0.500 0.045 11.006 0.000 0.411 0.589
## 83 tourn_no_m1 ~~ tourn_no_m1 0.647 0.053 12.104 0.000 0.542 0.752
## 84 alt_m3 ~~ alt_m3 0.987 0.408 2.417 0.016 0.187 1.787
## 85 wbc_m3 ~~ wbc_m3 0.943 0.244 3.869 0.000 0.465 1.421
## 86 lymph_m3 ~~ lymph_m3 0.877 0.083 10.608 0.000 0.715 1.039
## 87 max_hct_m3 ~~ max_hct_m3 0.880 0.099 8.869 0.000 0.686 1.075
## 88 platelets_m3 ~~ platelets_m3 0.914 0.090 10.187 0.000 0.738 1.089
## 89 tourn_no_m3 ~~ tourn_no_m3 0.983 0.060 16.407 0.000 0.865 1.100
## 90 ast_m3 ~~ ast_m3 0.996 0.428 2.329 0.020 0.158 1.834
## 91 dhf ~~ ast_m1 0.017 0.023 0.746 0.456 -0.028 0.063
## 92 dhf ~~ wbc_m1 0.019 0.027 0.691 0.490 -0.035 0.073
## 93 dhf ~~ albumin_m1 -0.018 0.045 -0.404 0.686 -0.106 0.070
## 94 dhf ~~ tourn_no_m1 0.054 0.041 1.311 0.190 -0.027 0.134
## 95 ast_m1 ~~ wbc_m1 -0.010 0.016 -0.604 0.546 -0.041 0.022
## 96 ast_m1 ~~ tourn_no_m1 0.001 0.016 0.075 0.940 -0.029 0.032
## 97 wbc_m1 ~~ albumin_m1 0.022 0.033 0.662 0.508 -0.043 0.087
## 98 wbc_m1 ~~ tourn_no_m1 -0.019 0.027 -0.719 0.472 -0.071 0.033
## 99 albumin_m1 ~~ tourn_no_m1 -0.026 0.038 -0.666 0.506 -0.101 0.050
## 100 albumin_m3 ~~ albumin_m3 0.996 0.102 9.727 0.000 0.795 1.197
## 101 albumin_m3 ~~ age_t 0.068 0.060 1.136 0.256 -0.050 0.186
## 102 age_t ~~ age_t 0.996 0.068 14.642 0.000 0.863 1.129
## std.lv std.all std.nox
## 1 0.160 0.160 0.160
## 2 -0.107 -0.107 -0.107
## 3 0.197 0.199 0.199
## 4 -0.243 -0.241 -0.241
## 5 -0.250 -0.252 -0.252
## 6 -0.056 -0.056 -0.056
## 7 -0.161 -0.162 -0.162
## 8 -0.042 -0.042 -0.042
## 9 -0.137 -0.137 -0.137
## 10 -0.073 -0.074 -0.074
## 11 0.749 0.752 0.752
## 12 0.271 0.275 0.275
## 13 -0.071 -0.072 -0.072
## 14 -0.093 -0.094 -0.094
## 15 -0.068 -0.068 -0.068
## 16 -0.093 -0.094 -0.094
## 17 0.445 0.449 0.449
## 18 0.223 0.222 0.222
## 19 -0.100 -0.100 -0.100
## 20 0.807 0.797 0.797
## 21 0.129 0.129 0.129
## 22 -0.104 -0.104 -0.104
## 23 -0.054 -0.054 -0.054
## 24 -0.199 -0.198 -0.198
## 25 0.281 0.281 0.281
## 26 -0.079 -0.080 -0.080
## 27 -0.175 -0.176 -0.176
## 28 -0.108 -0.110 -0.110
## 29 0.008 0.008 0.008
## 30 0.501 0.510 0.511
## 31 0.104 0.106 0.106
## 32 -0.106 -0.105 -0.105
## 33 -0.147 -0.146 -0.146
## 34 -0.071 -0.071 -0.071
## 35 0.498 0.497 0.497
## 36 0.178 0.178 0.179
## 37 0.312 0.315 0.315
## 38 0.085 0.086 0.086
## 39 0.519 0.527 0.527
## 40 0.125 0.127 0.127
## 41 -0.132 -0.134 -0.134
## 42 -0.136 -0.138 -0.138
## 43 -0.074 -0.075 -0.075
## 44 0.464 0.472 0.472
## 45 0.114 0.116 0.116
## 46 0.127 0.126 0.127
## 47 -0.192 -0.193 -0.194
## 48 -0.345 -0.345 -0.345
## 49 0.341 0.341 0.342
## 50 -0.280 -0.281 -0.281
## 51 0.116 0.116 0.116
## 52 0.365 0.711 0.711
## 53 0.118 0.188 0.188
## 54 -0.063 -0.108 -0.108
## 55 0.094 0.167 0.167
## 56 -0.036 -0.069 -0.069
## 57 -0.108 -0.199 -0.199
## 58 0.115 0.264 0.264
## 59 -0.113 -0.160 -0.160
## 60 0.157 0.267 0.267
## 61 -0.111 -0.206 -0.206
## 62 0.108 0.175 0.175
## 63 -0.056 -0.099 -0.099
## 64 -0.162 -0.167 -0.167
## 65 -0.184 -0.193 -0.193
## 66 -0.118 -0.123 -0.123
## 67 -0.095 -0.101 -0.101
## 68 0.743 0.750 0.750
## 69 -0.379 -0.417 -0.417
## 70 0.299 0.323 0.323
## 71 -0.178 -0.185 -0.185
## 72 -0.153 -0.171 -0.171
## 73 0.137 0.148 0.148
## 74 -0.078 -0.087 -0.087
## 75 0.804 0.820 0.820
## 76 0.571 0.577 0.577
## 77 0.462 0.472 0.472
## 78 0.382 0.381 0.381
## 79 0.768 0.775 0.775
## 80 0.689 0.716 0.716
## 81 0.587 0.587 0.587
## 82 0.500 0.519 0.519
## 83 0.647 0.672 0.672
## 84 0.987 0.984 0.984
## 85 0.943 0.963 0.963
## 86 0.877 0.881 0.881
## 87 0.880 0.883 0.883
## 88 0.914 0.921 0.921
## 89 0.983 0.987 0.987
## 90 0.996 1.000 1.000
## 91 0.017 0.026 0.026
## 92 0.019 0.034 0.034
## 93 -0.018 -0.024 -0.024
## 94 0.054 0.074 0.074
## 95 -0.010 -0.021 -0.021
## 96 0.001 0.002 0.002
## 97 0.022 0.043 0.043
## 98 -0.019 -0.038 -0.038
## 99 -0.026 -0.038 -0.038
## 100 0.996 1.000 0.996
## 101 0.068 0.069 0.068
## 102 0.996 1.000 0.996
Residual covariances
lavResiduals(fit,zstat=TRUE, type='cor')
## $type
## [1] "cor.bollen"
##
## $cov
## dhf ast_m1 alt_m1 wbc_m1 lymp_1 albm_1 mx_h_1 pltl_1 trn__1
## dhf 0.000
## ast_m1 0.031 0.000
## alt_m1 0.027 0.002 0.000
## wbc_m1 -0.044 -0.044 -0.033 0.000
## lymph_m1 0.000 -0.014 -0.040 -0.011 0.000
## albumin_m1 0.011 -0.087 -0.099 -0.016 0.036 0.000
## max_hct_m1 0.010 -0.016 0.021 -0.018 0.028 0.038 0.000
## platelets_m1 -0.020 -0.068 -0.071 0.016 0.001 0.036 -0.037 0.000
## tourn_no_m1 0.105 0.065 0.067 0.005 -0.028 -0.051 -0.014 -0.065 0.000
## alt_m3 0.021 0.007 0.004 0.009 -0.026 -0.105 0.023 -0.052 0.020
## wbc_m3 -0.060 -0.039 -0.027 -0.011 -0.006 0.017 -0.007 -0.006 -0.018
## lymph_m3 0.047 0.080 0.066 0.016 0.005 -0.037 -0.007 -0.011 0.026
## max_hct_m3 -0.067 0.073 0.100 0.007 -0.019 0.013 0.001 -0.029 0.050
## platelets_m3 0.041 -0.009 -0.012 0.060 0.002 0.094 -0.062 0.025 -0.067
## tourn_no_m3 0.171 0.085 0.071 0.016 -0.069 -0.092 -0.009 -0.080 0.028
## albumin_m3 0.041 -0.109 -0.144 0.005 0.014 0.023 0.079 0.091 -0.036
## age_t -0.008 0.033 0.041 -0.009 0.000 0.042 0.003 -0.018 -0.008
## ast_m3 0.062 0.012 0.008 -0.009 -0.022 -0.119 -0.065 -0.061 0.053
## alt_m3 wbc_m3 lymp_3 mx_h_3 pltl_3 trn__3 albm_3 age_t ast_m3
## dhf
## ast_m1
## alt_m1
## wbc_m1
## lymph_m1
## albumin_m1
## max_hct_m1
## platelets_m1
## tourn_no_m1
## alt_m3 0.000
## wbc_m3 -0.006 0.000
## lymph_m3 0.029 -0.015 0.000
## max_hct_m3 0.075 -0.010 -0.031 0.000
## platelets_m3 -0.002 0.011 -0.022 -0.009 0.000
## tourn_no_m3 0.030 -0.023 0.003 0.056 -0.048 0.000
## albumin_m3 -0.176 0.066 -0.094 0.139 0.180 -0.032 0.000
## age_t -0.026 0.007 0.000 0.000 0.007 0.000 0.000 0.000
## ast_m3 -0.002 -0.043 0.100 0.092 -0.011 0.119 -0.189 -0.036 0.000
##
## $cov.z
## dhf ast_m1 alt_m1 wbc_m1 lymp_1 albm_1 mx_h_1 pltl_1 trn__1
## dhf 0.000
## ast_m1 1.006 0.000
## alt_m1 1.151 0.191 0.000
## wbc_m1 -1.125 -1.540 -1.025 0.000
## lymph_m1 -0.016 -0.151 -0.559 -0.567 0.000
## albumin_m1 0.294 -3.972 -3.232 -0.368 0.581 0.000
## max_hct_m1 0.560 -0.380 0.434 -0.462 0.579 0.625 0.000
## platelets_m1 -1.175 -1.338 -1.476 0.632 0.020 1.216 -0.956 0.000
## tourn_no_m1 2.984 1.930 1.852 0.230 -1.048 -1.454 -0.380 -1.568 0.000
## alt_m3 0.354 0.342 0.366 0.435 -0.445 -2.308 0.353 -1.235 0.518
## wbc_m3 -1.485 -2.217 -1.529 -2.364 -0.720 0.308 -0.306 -0.460 -1.621
## lymph_m3 0.778 2.271 1.644 1.572 0.440 -0.629 -0.268 -0.643 2.744
## max_hct_m3 -1.028 0.506 0.805 0.125 -0.669 0.204 0.017 -0.579 0.815
## platelets_m3 0.928 -0.474 -0.576 1.443 0.039 3.050 -1.340 2.331 -1.217
## tourn_no_m3 2.626 1.843 1.518 0.355 -1.207 -1.495 -0.160 -1.294 2.422
## albumin_m3 0.680 -2.000 -2.362 0.147 0.234 1.412 1.397 1.657 -0.972
## age_t -0.140 0.657 0.703 -0.755 -0.043 0.815 0.264 -0.426 -0.929
## ast_m3 1.210 0.837 0.848 -0.339 -0.292 -3.309 -0.949 -1.098 1.468
## alt_m3 wbc_m3 lymp_3 mx_h_3 pltl_3 trn__3 albm_3 age_t ast_m3
## dhf
## ast_m1
## alt_m1
## wbc_m1
## lymph_m1
## albumin_m1
## max_hct_m1
## platelets_m1
## tourn_no_m1
## alt_m3 0.000
## wbc_m3 -0.296 0.000
## lymph_m3 0.587 -1.666 0.000
## max_hct_m3 0.822 -0.227 -0.592 0.000
## platelets_m3 -0.083 0.887 -0.996 -0.276 0.000
## tourn_no_m3 0.588 -0.991 0.138 0.925 -0.779 0.000
## albumin_m3 -2.076 1.407 -1.622 2.292 2.769 -0.512 0.000
## age_t -0.578 0.921 0.017 0.000 0.534 0.000 0.000 0.000
## ast_m3 -0.244 -1.934 1.880 0.542 -0.331 2.028 -2.078 -0.601 0.000
##
## $summary
## cov
## crmr 0.056
## crmr.se 0.012
## crmr.exactfit.z 0.841
## crmr.exactfit.pvalue 0.200
## ucrmr 0.031
## ucrmr.se 0.016
## ucrmr.ci.lower 0.005
## ucrmr.cilupper 0.058
## ucrmr.closefit.h0.value 0.050
## ucrmr.closefit.z -1.171
## ucrmr.closefit.pvalue 0.879
Modification indices
To adjust further the model, one useful output is the modification indices:
modificationindices(fit,standardized = TRUE)%>%arrange(-mi)%>%head()
## lhs op rhs mi epc sepc.lv sepc.all sepc.nox
## 1 albumin_m3 ~ alt_m1 11.127 -0.292 -0.292 -0.290 -0.290
## 2 max_hct_m1 ~~ ast_m3 11.125 -0.100 -0.100 -0.131 -0.131
## 3 albumin_m3 ~ platelets_m3 9.104 0.196 0.196 0.196 0.196
## 4 albumin_m3 ~ ast_m3 8.962 -0.186 -0.186 -0.186 -0.186
## 5 albumin_m3 ~ alt_m3 7.908 -0.176 -0.176 -0.176 -0.176
## 6 dhf ~ tourn_no_m1 7.714 0.305 0.305 0.302 0.302