目录
Overview
本教程将在几个不同的框架（如多层次模型框架、结构方程模型框架）中进行线性增长模型的拟合，并使用不同的R包演示这些模型（在尝试拟合更复杂的模型时，了解如何在不同的包中拟合模型会有帮助，因为每个包都有自己的优势和限制）。在本教程中，我们将使用一个样本数据集，其中包括对个人在小学和初中的数学成绩的重复测量。
本教程中提供的代码和例子来自Grimm, Ram, and Estabrook (2016)的第三章，在代码和评论中做了一些补充说明。关于分析的进一步解释和见解，请参考该章。
第0步：读入数据并调用需要的库。
#set filepath
filepath<-"https://quantdev.ssri.psu.edu/sites/qdev/files/nlsy_math_long_R.csv"
#read in the .csv file using the url() function
nlsy_math_long <- read.csv(file=url(filepath),header=TRUE)
#add names the columns of the data set
names(nlsy_math_long) <- c('id', 'female', 'low_birth_weight', 'anti_k1', 'math', 'grade', 'occ', 'age', 'men', 'spring', 'anti')
#view the first few observations in the data set
head(nlsy_math_long)## id female low_birth_weight anti_k1 math grade occ age men spring anti
## 1 201 1 0 0 38 3 2 111 0 1 0
## 2 201 1 0 0 55 5 3 135 1 1 0
## 3 303 1 0 1 26 2 2 121 0 1 2
## 4 303 1 0 1 33 5 3 145 0 1 2
## 5 2702 0 0 0 56 2 2 100 NA 1 0
## 6 2702 0 0 0 58 4 3 125 NA 1 2#allows for objects in the data set to be accessed be name
attach(nlsy_math_long)
#calling the libraries we will need throughout this tutorial
library(ggplot2)
library(lavaan)
library(lme4)
library(nlme)第1步：绘制纵向数据。
为更好地理解观察到的现象的结构和形式，绘制数据是很重要的。在这里，我们要检查数据，以确保增长模型是对数据的适当分析（也就是说，我们需要检查是否真的有增长可以建模）。
#creating a plot and assigning it to an object
plot_obs <- ggplot(data=nlsy_math_long, #data set
aes(x = grade, y = math, group = id)) + #calling variables
geom_line() + #adding lines to plot
theme_bw() + #changing style/background
scale_x_continuous(breaks = 2:8, name = "Grade") + #creating breaks in the x-axis and labeling the x-axis
scale_y_continuous(name = "PIAT Mathematics") #creating breaks in the y-axis and labeling the y-axis
#print the object (plot)
print(plot_obs)
第2步：拟合一个无增长模型
从我们上面的图中可以看出，数学成绩似乎随着时间的推移有所增长。为了开始分析，我们将拟合一个无增长模型。这个无增长模型将作为我们的 "空 "模型，与后面的模型进行比较。
使用 "lme "函数的无增长模型
#fitting no growth model and assigning it to an object
ng.math.lme <- lme(math ~ 1, random= ~1 |id, data = nlsy_math_long, method="ML")
#obtaining summary of the model using the object we just created
summary(ng.math.lme)## Linear mixed-effects model fit by maximum likelihood
## Data: nlsy_math_long
## AIC BIC logLik
## 17497.9 17515.02 -8745.952
##
## Random effects:
## Formula: ~1 | id
## (Intercept) Residual
## StdDev: 6.849591 10.80195
##
## Fixed effects: math ~ 1
## Value Std.Error DF t-value p-value
## (Intercept) 45.91468 0.3237961 1289 141.8012 0
##
## Standardized Within-Group Residuals:
## Min Q1 Med Q3 Max
## -2.79834566 -0.57828004 0.05407981 0.57885522 2.52690025
##
## Number of Observations: 2221
## Number of Groups: 932#obtaining confidence intervals of model parameters
intervals(ng.math.lme)## Approximate 95% confidence intervals
##
## Fixed effects:
## lower est. upper
## (Intercept) 45.2796 45.91468 46.54977
## attr(,"label")
## [1] "Fixed effects:"
##
## Random Effects:
## Level: id
## lower est. upper
## sd((Intercept)) 6.19195 6.849591 7.577078
##
## Within-group standard error:
## lower est. upper
## 10.39711 10.80195 11.22255使用 "nlme "函数的无增长模型
#fitting no growth model and assigning it to an object
ng.math.nlme <- nlme(math ~ beta_1 + d_1i,
data=nlsy_math_long,
fixed=beta_1~1,
random=d_1i~1,
group=~id,
start=c(beta_1=40),
na.action = "na.exclude")
#obtaining summary of the model using the object we just created
summary(ng.math.nlme)## Nonlinear mixed-effects model fit by maximum likelihood
## Model: math ~ beta_1 + d_1i
## Data: nlsy_math_long
## AIC BIC logLik
## 17497.9 17515.02 -8745.952
##
## Random effects:
## Formula: d_1i ~ 1 | id
## d_1i Residual
## StdDev: 6.849581 10.80196
##
## Fixed effects: beta_1 ~ 1
## Value Std.Error DF t-value p-value
## beta_1 45.91468 0.323796 1289 141.8013 0
##
## Standardized Within-Group Residuals:
## Min Q1 Med Q3 Max
## -2.79834502 -0.57827917 0.05408079 0.57885591 2.52690020
##
## Number of Observations: 2221
## Number of Groups: 932在 "nlme "函数中使用替代规格的无增长模型
#fitting no growth model and assigning it to an object
ng.math.nlme <- nlme(math~b_1i,
data=nlsy_math_long,
fixed=b_1i~1,
random=b_1i~1|id,
start=c(b_1i=40),
na.action = "na.exclude")
#obtaining summary of the model using the object we just created
summary(ng.math.nlme)## Nonlinear mixed-effects model fit by maximum likelihood
## Model: math ~ b_1i
## Data: nlsy_math_long
## AIC BIC logLik
## 17497.9 17515.02 -8745.952
##
## Random effects:
## Formula: b_1i ~ 1 | id
## b_1i Residual
## StdDev: 6.849582 10.80196
##
## Fixed effects: b_1i ~ 1
## Value Std.Error DF t-value p-value
## b_1i 45.91468 0.323796 1289 141.8013 0
##
## Standardized Within-Group Residuals:
## Min Q1 Med Q3 Max
## -2.79834512 -0.57827919 0.05408079 0.57885592 2.52690029
##
## Number of Observations: 2221
## Number of Groups: 932使用 lme4包"lmer "函数的无增长模型
#fitting no growth model and assigning it to an object
ng.math.lmer <- lmer(math ~ 1 + (1 | id),
data = nlsy_math_long,
REML = FALSE,
na.action = "na.exclude")
#obtaining summary of the model using the object we just created
summary(ng.math.lmer)## Linear mixed model fit by maximum likelihood ['lmerMod']
## Formula: math ~ 1 + (1 | id)
## Data: nlsy_math_long
##
## AIC BIC logLik deviance df.resid
## 17497.9 17515.0 -8746.0 17491.9 2218
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.79835 -0.57828 0.05408 0.57886 2.52690
##
## Random effects:
## Groups Name Variance Std.Dev.
## id (Intercept) 46.92 6.85
## Residual 116.68 10.80
## Number of obs: 2221, groups: id, 932
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 45.9147 0.3237 141.8使用 lavaan包的无增长模型
首先，我们需要将数据从长数据重塑为宽数据。
names(nlsy_math_long)## [1] "id" "female" "low_birth_weight"
## [4] "anti_k1" "math" "grade"
## [7] "occ" "age" "men"
## [10] "spring" "anti"# names of variables in data
#c("id","female","low_birth_weight","anti_k1","math","grade","occ","age","men","spring","anti")
nlsy_math_wide <- reshape(data=nlsy_math_long,
timevar=c("grade"),
idvar=c("id"),
v.names=c("math","occ","age","men","spring","anti"),
direction="wide", sep="_")
#view the first few observations in the data set
head(nlsy_math_wide)## id female low_birth_weight anti_k1 math_3 occ_3 age_3 men_3 spring_3
## 1 201 1 0 0 38 2 111 0 1
## 3 303 1 0 1 NA NA NA NA NA
## 5 2702 0 0 0 NA NA NA NA NA
## 8 4303 1 0 0 41 2 115 0 0
## 10 5002 0 0 4 NA NA NA NA NA
## 13 5005 1 0 0 NA NA NA NA NA
## anti_3 math_5 occ_5 age_5 men_5 spring_5 anti_5 math_2 occ_2 age_2
## 1 0 55 3 135 1 1 0 NA NA NA
## 3 NA 33 3 145 0 1 2 26 2 121
## 5 NA NA NA NA NA NA NA 56 2 100
## 8 1 NA NA NA NA NA NA NA NA NA
## 10 NA NA NA NA NA NA NA NA NA NA
## 13 NA NA NA NA NA NA NA 35 2 93
## men_2 spring_2 anti_2 math_4 occ_4 age_4 men_4 spring_4 anti_4 math_8
## 1 NA NA NA NA NA NA NA NA NA NA
## 3 0 1 2 NA NA NA NA NA NA NA
## 5 NA 1 0 58 3 125 NA 1 2 80
## 8 NA NA NA 58 3 135 0 1 2 NA
## 10 NA NA NA 46 2 117 NA 1 4 66
## 13 0 0 2 50 3 115 0 1 2 59
## occ_8 age_8 men_8 spring_8 anti_8 math_6 occ_6 age_6 men_6 spring_6
## 1 NA NA NA NA NA NA NA NA NA NA
## 3 NA NA NA NA NA NA NA NA NA NA
## 5 4 173 NA 1 2 NA NA NA NA NA
## 8 NA NA NA NA NA NA NA NA NA NA
## 10 4 167 NA 1 5 54 3 145 NA 0
## 13 5 163 1 1 3 60 4 139 0 1
## anti_6 math_7 occ_7 age_7 men_7 spring_7 anti_7
## 1 NA NA NA NA NA NA NA
## 3 NA NA NA NA NA NA NA
## 5 NA NA NA NA NA NA NA
## 8 NA NA NA NA NA NA NA
## 10 1 NA NA NA NA NA NA
## 13 1 NA NA NA NA NA NA#might engage in a bit of reordering for easy viewing现在，我们把无增长模型设定为一个lavaan模型
#writing out no growth model in full SEM way
ng.math.lavaan_model <- '
# latent variable definitions
#intercept
eta_1 =~ 1*math_2
eta_1 =~ 1*math_3
eta_1 =~ 1*math_4
eta_1 =~ 1*math_5
eta_1 =~ 1*math_6
eta_1 =~ 1*math_7
eta_1 =~ 1*math_8
# factor variances
eta_1 ~~ eta_1
# covariances among factors
#none (only 1 factor)
# factor means
eta_1 ~ start(30)*1
# manifest variances (made equivalent by naming theta)
math_2 ~~ theta*math_2
math_3 ~~ theta*math_3
math_4 ~~ theta*math_4
math_5 ~~ theta*math_5
math_6 ~~ theta*math_6
math_7 ~~ theta*math_7
math_8 ~~ theta*math_8
# manifest means (fixed at zero)
math_2 ~ 0*1
math_3 ~ 0*1
math_4 ~ 0*1
math_5 ~ 0*1
math_6 ~ 0*1
math_7 ~ 0*1
math_8 ~ 0*1
' #end of model definition并将模型与数据进行拟合......。
#estimating the model using sem() function
ng.math.lavaan_fit <- sem(ng.math.lavaan_model,
data = nlsy_math_wide,
meanstructure = TRUE,
estimator = "ML",
missing = "fiml")## Warning in lav_data_full(data = data, group = group, group.label =
## group.label, : lavaan WARNING: due to missing values, some pairwise
## combinations have less than 10% coveragesummary(ng.math.lavaan_fit)## lavaan (0.5-22) converged normally after 18 iterations
##
## Number of observations 932
##
## Number of missing patterns 60
##
## Estimator ML
## Minimum Function Test Statistic 1759.002
## Degrees of freedom 32
## P-value (Chi-square) 0.000
##
## Parameter Estimates:
##
## Information Observed
## Standard Errors Standard
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|)
## eta_1 =~
## math_2 1.000
## math_3 1.000
## math_4 1.000
## math_5 1.000
## math_6 1.000
## math_7 1.000
## math_8 1.000
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|)
## eta_1 45.915 0.324 141.721 0.000
## .math_2 0.000
## .math_3 0.000
## .math_4 0.000
## .math_5 0.000
## .math_6 0.000
## .math_7 0.000
## .math_8 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|)
## eta_1 46.917 4.832 9.709 0.000
## .math_2 (thet) 116.682 4.548 25.656 0.000
## .math_3 (thet) 116.682 4.548 25.656 0.000
## .math_4 (thet) 116.682 4.548 25.656 0.000
## .math_5 (thet) 116.682 4.548 25.656 0.000
## .math_6 (thet) 116.682 4.548 25.656 0.000
## .math_7 (thet) 116.682 4.548 25.656 0.000
## .math_8 (thet) 116.682 4.548 25.656 0.000fitMeasures(ng.math.lavaan_fit)## npar fmin chisq
## 3.000 0.944 1759.002
## df pvalue baseline.chisq
## 32.000 0.000 862.333
## baseline.df baseline.pvalue cfi
## 21.000 0.000 0.000
## tli nnfi rfi
## -0.347 -0.347 1.000
## nfi pnfi ifi
## -1.040 -1.584 -1.080
## rni logl unrestricted.logl
## -1.053 -8745.952 -7866.451
## aic bic ntotal
## 17497.903 17512.415 932.000
## bic2 rmsea rmsea.ci.lower
## 17502.888 0.241 0.231
## rmsea.ci.upper rmsea.pvalue rmr
## 0.250 0.000 38.332
## rmr_nomean srmr srmr_bentler
## 38.332 0.480 0.480
## srmr_bentler_nomean srmr_bollen srmr_bollen_nomean
## 0.362 0.624 0.339
## srmr_mplus srmr_mplus_nomean cn_05
## 0.675 0.444 25.476
## cn_01 gfi agfi
## 29.339 0.937 0.931
## pgfi mfi ecvi
## 0.856 0.396 NA#Other summaries
#parameterEstimates(ng.math.lavaan_fit)
#inspect(ng.math.lavaan_fit, what="est")第3步：拟合一个线性增长模型。
接下来，我们使用并比较了几个不同的函数和软件包来拟合一个线性增长模型。
#creating object with what was originally grade 2 as now the zero (starting) point
grade_c2 <- grade - 2使用‘lme’函数构建线性增长模型
#fitting linear growth model and assigning it to an object
lg.math.lme <- lme(math ~ grade_c2, random= ~ grade_c2 |id, data = nlsy_math_long, method="ML")
#obtaining summary of the model using the object we just created
summary(lg.math.lme)## Linear mixed-effects model fit by maximum likelihood
## Data: nlsy_math_long
## AIC BIC logLik
## 15949.39 15983.62 -7968.693
##
## Random effects:
## Formula: ~grade_c2 | id
## Structure: General positive-definite, Log-Cholesky parametrization
## StdDev Corr
## (Intercept) 8.035040 (Intr)
## grade_c2 0.855900 -0.026
## Residual 6.019114
##
## Fixed effects: math ~ grade_c2
## Value Std.Error DF t-value p-value
## (Intercept) 35.26736 0.3551568 1288 99.30081 0
## grade_c2 4.33933 0.0873767 1288 49.66231 0
## Correlation:
## (Intr)
## grade_c2 -0.532
##
## Standardized Within-Group Residuals:
## Min Q1 Med Q3 Max
## -3.030277540 -0.525876497 0.001633029 0.540751608 2.542250503
##
## Number of Observations: 2221
## Number of Groups: 932使用‘nlme’函数构建线性增长模型
#fitting linear growth model and assigning it to an object
lg.math.nlme <- nlme(math~(beta_1+d_1i)+(beta_2+d_2i)*(grade-2),
data=nlsy_math_long,
fixed=beta_1+beta_2~1,
random=d_1i+d_2i~1,
group=~id,
start=c(beta_1=35,beta_2=4),
na.action = "na.exclude")
#obtaining summary of the model using the object we just created
summary (lg.math.nlme)## Nonlinear mixed-effects model fit by maximum likelihood
## Model: math ~ (beta_1 + d_1i) + (beta_2 + d_2i) * (grade - 2)
## Data: nlsy_math_long
## AIC BIC logLik
## 15949.39 15983.62 -7968.693
##
## Random effects:
## Formula: list(d_1i ~ 1, d_2i ~ 1)
## Level: id
## Structure: General positive-definite, Log-Cholesky parametrization
## StdDev Corr
## d_1i 8.0350382 d_1i
## d_2i 0.8558994 -0.026
## Residual 6.0191140
##
## Fixed effects: beta_1 + beta_2 ~ 1
## Value Std.Error DF t-value p-value
## beta_1 35.26736 0.3551568 1288 99.30082 0
## beta_2 4.33933 0.0873767 1288 49.66231 0
## Correlation:
## beta_1
## beta_2 -0.532
##
## Standardized Within-Group Residuals:
## Min Q1 Med Q3 Max
## -3.030277731 -0.525876489 0.001632883 0.540751587 2.542250204
##
## Number of Observations: 2221
## Number of Groups: 932在 "nlme "函数中使用替代规格的无增长模型
#fitting linear growth model and assigning it to an object
lg.math.nlme <- nlme(math~b_1i+b_2i*(grade-2),
data=nlsy_math_long,
fixed=b_1i+b_2i~1,
random=b_1i+b_2i~1|id,
start=c(b_1i=35, b_2i=4))
#obtaining summary of the model using the object we just created
summary(lg.math.nlme)## Nonlinear mixed-effects model fit by maximum likelihood
## Model: math ~ b_1i + b_2i * (grade - 2)
## Data: nlsy_math_long
## AIC BIC logLik
## 15949.39 15983.62 -7968.693
##
## Random effects:
## Formula: list(b_1i ~ 1, b_2i ~ 1)
## Level: id
## Structure: General positive-definite, Log-Cholesky parametrization
## StdDev Corr
## b_1i 8.0350377 b_1i
## b_2i 0.8558995 -0.026
## Residual 6.0191139
##
## Fixed effects: b_1i + b_2i ~ 1
## Value Std.Error DF t-value p-value
## b_1i 35.26736 0.3551567 1288 99.30083 0
## b_2i 4.33933 0.0873767 1288 49.66231 0
## Correlation:
## b_1i
## b_2i -0.532
##
## Standardized Within-Group Residuals:
## Min Q1 Med Q3 Max
## -3.030277750 -0.525876492 0.001632883 0.540751591 2.542250220
##
## Number of Observations: 2221
## Number of Groups: 932使用‘lme4’包构建线性增长模型
#fitting linear growth model and assigning it to an object
lg.math.lmer <- lmer(math ~ 1 + grade_c2 + (1 + grade_c2 | id), data = nlsy_math_long, REML = FALSE)
#obtaining summary of the model using the object we just created
summary(lg.math.lmer)## Linear mixed model fit by maximum likelihood ['lmerMod']
## Formula: math ~ 1 + grade_c2 + (1 + grade_c2 | id)
## Data: nlsy_math_long
##
## AIC BIC logLik deviance df.resid
## 15949.4 15983.6 -7968.7 15937.4 2215
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.03028 -0.52588 0.00163 0.54075 2.54225
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## id (Intercept) 64.5618 8.0350
## grade_c2 0.7326 0.8559 -0.03
## Residual 36.2297 6.0191
## Number of obs: 2221, groups: id, 932
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 35.26736 0.35500 99.35
## grade_c2 4.33933 0.08734 49.68
##
## Correlation of Fixed Effects:
## (Intr)
## grade_c2 -0.532使用‘lavaan’包构建线性增长模型
#writing out linear growth model in full SEM way
lg.math.lavaan_model <- '
# latent variable definitions
#intercept (note intercept is a reserved term)
eta_1 =~ 1*math_2
eta_1 =~ 1*math_3
eta_1 =~ 1*math_4
eta_1 =~ 1*math_5
eta_1 =~ 1*math_6
eta_1 =~ 1*math_7
eta_1 =~ 1*math_8
#linear slope (note intercept is a reserved term)
eta_2 =~ 0*math_2
eta_2 =~ 1*math_3
eta_2 =~ 2*math_4
eta_2 =~ 3*math_5
eta_2 =~ 4*math_6
eta_2 =~ 5*math_7
eta_2 =~ 6*math_8
# factor variances
eta_1 ~~ eta_1
eta_2 ~~ eta_2
# covariances among factors
eta_1 ~~ eta_2
# factor means
eta_1 ~ start(35)*1
eta_2 ~ start(4)*1
# manifest variances (made equivalent by naming theta)
math_2 ~~ theta*math_2
math_3 ~~ theta*math_3
math_4 ~~ theta*math_4
math_5 ~~ theta*math_5
math_6 ~~ theta*math_6
math_7 ~~ theta*math_7
math_8 ~~ theta*math_8
# manifest means (fixed at zero)
math_2 ~ 0*1
math_3 ~ 0*1
math_4 ~ 0*1
math_5 ~ 0*1
math_6 ~ 0*1
math_7 ~ 0*1
math_8 ~ 0*1
' #end of model definition并将模型与数据进行拟合......。
#estimating the model using sem() function
lg.math.lavaan_fit <- sem(lg.math.lavaan_model,
data = nlsy_math_wide,
meanstructure = TRUE,
estimator = "ML",
missing = "fiml")## Warning in lav_data_full(data = data, group = group, group.label =
## group.label, : lavaan WARNING: due to missing values, some pairwise
## combinations have less than 10% coveragesummary(lg.math.lavaan_fit)## lavaan (0.5-22) converged normally after 27 iterations
##
## Number of observations 932
##
## Number of missing patterns 60
##
## Estimator ML
## Minimum Function Test Statistic 204.484
## Degrees of freedom 29
## P-value (Chi-square) 0.000
##
## Parameter Estimates:
##
## Information Observed
## Standard Errors Standard
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|)
## eta_1 =~
## math_2 1.000
## math_3 1.000
## math_4 1.000
## math_5 1.000
## math_6 1.000
## math_7 1.000
## math_8 1.000
## eta_2 =~
## math_2 0.000
## math_3 1.000
## math_4 2.000
## math_5 3.000
## math_6 4.000
## math_7 5.000
## math_8 6.000
##
## Covariances:
## Estimate Std.Err z-value P(>|z|)
## eta_1 ~~
## eta_2 -0.181 1.150 -0.158 0.875
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|)
## eta_1 35.267 0.355 99.229 0.000
## eta_2 4.339 0.088 49.136 0.000
## .math_2 0.000
## .math_3 0.000
## .math_4 0.000
## .math_5 0.000
## .math_6 0.000
## .math_7 0.000
## .math_8 0.000
##
## Variances:
## Estimate Std.Err z-value P(>|z|)
## eta_1 64.562 5.659 11.408 0.000
## eta_2 0.733 0.327 2.238 0.025
## .math_2 (thet) 36.230 1.867 19.410 0.000
## .math_3 (thet) 36.230 1.867 19.410 0.000
## .math_4 (thet) 36.230 1.867 19.410 0.000
## .math_5 (thet) 36.230 1.867 19.410 0.000
## .math_6 (thet) 36.230 1.867 19.410 0.000
## .math_7 (thet) 36.230 1.867 19.410 0.000
## .math_8 (thet) 36.230 1.867 19.410 0.000fitMeasures(lg.math.lavaan_fit)## npar fmin chisq
## 6.000 0.110 204.484
## df pvalue baseline.chisq
## 29.000 0.000 862.333
## baseline.df baseline.pvalue cfi
## 21.000 0.000 0.791
## tli nnfi rfi
## 0.849 0.849 0.828
## nfi pnfi ifi
## 0.763 1.053 0.789
## rni logl unrestricted.logl
## 0.791 -7968.693 -7866.451
## aic bic ntotal
## 15949.386 15978.410 932.000
## bic2 rmsea rmsea.ci.lower
## 15959.354 0.081 0.070
## rmsea.ci.upper rmsea.pvalue rmr
## 0.091 0.000 10.840
## rmr_nomean srmr srmr_bentler
## 10.840 0.121 0.121
## srmr_bentler_nomean srmr_bollen srmr_bollen_nomean
## 0.097 0.174 0.076
## srmr_mplus srmr_mplus_nomean cn_05
## 0.179 0.088 194.967
## cn_01 gfi agfi
## 227.012 0.990 0.988
## pgfi mfi ecvi
## 0.820 0.910 NA#Other summaries
#parameterEstimates(ng.math.lavaan_fit)
#inspect(ng.math.lavaan_fit, what="est")第4步：获得并绘制预测和残差估计值。
我们继续使用上述 "nlme "函数的线性增长模型的结果，以获得和绘制数学成绩的预测轨迹和估计。
#obtaining individual estimates of the intercept and slope using fixed and random effects estimates and storing this information into objects
b_1i_hat <- ranef(lg.math.nlme)[,1] + fixef(lg.math.nlme)[1]
b_2i_hat <- ranef(lg.math.nlme)[,2] + fixef(lg.math.nlme)[2]
#creating list of ids from row names of the nlme linear model object
child_id <- as.numeric(rownames(ranef(lg.math.nlme)))
#creating new data set that contains information on each child's id, intercept estimate, and slope estimate
estimates <- data.frame(child_id, b_1i_hat, b_2i_hat)
#creating new data set by merging original data set with the estimates data set we just created
estimates1 = merge(x = nlsy_math_long, y = estimates,
by.x = c('id'), by.y = c('child_id'),
all = TRUE)
#creating new variables that calculate the predicted and residual mathematics achievement scores for each child
estimates1$pred = estimates1$b_1i_hat + estimates1$b_2i_hat * (estimates1$grade - 2)
estimates1$resid = estimates1$math - estimates1$pred
#creating a plot of predicted values and assigning it to an object
plot_pred <- ggplot(data=estimates1,
aes(x = grade, y = pred, group = id)) +
geom_line() +
theme_bw() +
scale_x_continuous(breaks = 2:8, name = "Grade") +
scale_y_continuous(name = "PIAT Mathematics - Predictions")
#printing the object (plot)
print(plot_pred)
#creating a plot of residual values and assigning it to an object
plot_resid <- ggplot(data=estimates1,
aes(x = grade, y = resid, group = id)) +
geom_line() +
theme_bw() +
scale_x_continuous(breaks = 2:8, name = "Grade") +
scale_y_continuous(name = "PIAT Mathematics - Predictions")
#printing the object (plot)
print(plot_resid)
detach(nlsy_math_long)结论
本教程介绍了几种建立和分析纵向数据的无增长和线性模型的方法，以及绘制这些模型的预测轨迹和残差。
ref:Chapter 3 - Linear Growth Model