# Load R Data File
# install.packages("readr")
# install.packages("dplyr")
# install.packages("psych")
# install.packages("TAM")
library(psych)
library(dplyr)
##
## Attaching package: 'dplyr'
## The following objects are masked from 'package:stats':
##
## filter, lag
## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, union
library(readr)
library(TAM)
## Loading required package: CDM
## Loading required package: mvtnorm
## **********************************
## ** CDM 8.2-6 (2022-08-25 15:43:23)
## ** Cognitive Diagnostic Models **
## **********************************
## * TAM 4.1-4 (2022-08-28 16:03:54)
data <- read_csv("hsls_17_student_pets_sr_v1_0.csv")
## Rows: 23503 Columns: 9614
## ── Column specification ────────────────────────────────────────────────────────
## Delimiter: ","
## chr (3): X2UNIV1, X3UNIV1, X4UNIV1
## dbl (9611): STU_ID, SCH_ID, X1NCESID, X2NCESID, STRAT_ID, PSU, X2UNIV2A, X2U...
##
## ℹ Use `spec()` to retrieve the full column specification for this data.
## ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.
# Define the SBI and HBI variables separately
sbi_vars <- cbind(data$P1SCHMTG, data$P1PTOMTG, data$P1PTCONFER,
data$P1SCHEVENT, data$P1VOLUNTEER,
data$P1FUNDRAISE, data$P1COUNSELOR,
data$P1SCIFAIR)
write.csv(sbi_vars, "sbi_data.csv")
hbi_vars <- cbind(data$P1MUSEUM, data$P1LIBRARY, data$P1SCIFAIR, data$P1COMPUTER, data$P1SHOW,
data$P1FIXED, data$P1SCIPROJ,
data$P1STEMDISC)
write.csv(hbi_vars, "hbi_data.csv")
# Rename the column names for SBI variables
colnames(sbi_vars) <- c("SBI_sch_mtg", "SBI_pto",
"SBI_pt_conf","SBI_sch_evnt",
"SBI_volntr", "SBI_fundr",
"SBI_counsl", "SBI_scifair")
# Remove -9 and -8 from the dataset
sbi_vars[sbi_vars == -9 | sbi_vars == -8] <- NA
sbi_vars = na.omit(sbi_vars)
# Rename the column names for HBI variables
colnames(hbi_vars) <- c("HBI_museum", "HBI_library",
"HBI_scifair",
"HBI_compute","HBI_show",
"HBI_fixed", "HBI_sciproj",
"HBI_stemdisc")
# Remove -9 and -8 from the dataset
hbi_vars[hbi_vars == -9 | hbi_vars == -8] <- NA
hbi_vars = na.omit(hbi_vars)
# Compute reliability analysis for SBI
sbi_reliability <- alpha(sbi_vars)
summary(sbi_reliability)
##
## Reliability analysis
## raw_alpha std.alpha G6(smc) average_r S/N ase mean sd median_r
## 0.68 0.68 0.67 0.21 2.1 0.0039 0.49 0.26 0.19
sbi_reliability
##
## Reliability analysis
## Call: alpha(x = sbi_vars)
##
## raw_alpha std.alpha G6(smc) average_r S/N ase mean sd median_r
## 0.68 0.68 0.67 0.21 2.1 0.0039 0.49 0.26 0.19
##
## 95% confidence boundaries
## lower alpha upper
## Feldt 0.67 0.68 0.69
## Duhachek 0.67 0.68 0.69
##
## Reliability if an item is dropped:
## raw_alpha std.alpha G6(smc) average_r S/N alpha se var.r med.r
## SBI_sch_mtg 0.65 0.65 0.63 0.21 1.8 0.0043 0.0092 0.18
## SBI_pto 0.64 0.64 0.62 0.20 1.8 0.0044 0.0094 0.17
## SBI_pt_conf 0.65 0.65 0.63 0.21 1.8 0.0043 0.0093 0.19
## SBI_sch_evnt 0.64 0.64 0.61 0.20 1.7 0.0045 0.0065 0.18
## SBI_volntr 0.63 0.63 0.61 0.19 1.7 0.0046 0.0061 0.19
## SBI_fundr 0.63 0.63 0.61 0.20 1.7 0.0045 0.0052 0.19
## SBI_counsl 0.68 0.68 0.66 0.23 2.1 0.0039 0.0075 0.21
## SBI_scifair 0.68 0.68 0.66 0.23 2.1 0.0040 0.0076 0.23
##
## Item statistics
## n raw.r std.r r.cor r.drop mean sd
## SBI_sch_mtg 15164 0.53 0.56 0.45 0.38 0.83 0.37
## SBI_pto 15164 0.60 0.59 0.50 0.41 0.38 0.49
## SBI_pt_conf 15164 0.57 0.56 0.45 0.37 0.57 0.50
## SBI_sch_evnt 15164 0.60 0.60 0.52 0.42 0.69 0.46
## SBI_volntr 15164 0.63 0.62 0.56 0.46 0.31 0.46
## SBI_fundr 15164 0.62 0.61 0.55 0.43 0.53 0.50
## SBI_counsl 15164 0.47 0.46 0.31 0.25 0.43 0.50
## SBI_scifair 15164 0.40 0.44 0.28 0.23 0.18 0.38
##
## Non missing response frequency for each item
## 0 1 miss
## SBI_sch_mtg 0.17 0.83 0
## SBI_pto 0.62 0.38 0
## SBI_pt_conf 0.43 0.57 0
## SBI_sch_evnt 0.31 0.69 0
## SBI_volntr 0.69 0.31 0
## SBI_fundr 0.47 0.53 0
## SBI_counsl 0.57 0.43 0
## SBI_scifair 0.82 0.18 0
# Compute reliability analysis for HBI
hbi_reliability <- alpha(hbi_vars)
summary(hbi_reliability)
##
## Reliability analysis
## raw_alpha std.alpha G6(smc) average_r S/N ase mean sd median_r
## 0.58 0.58 0.56 0.15 1.4 0.0051 0.54 0.23 0.14
hbi_reliability
##
## Reliability analysis
## Call: alpha(x = hbi_vars)
##
## raw_alpha std.alpha G6(smc) average_r S/N ase mean sd median_r
## 0.58 0.58 0.56 0.15 1.4 0.0051 0.54 0.23 0.14
##
## 95% confidence boundaries
## lower alpha upper
## Feldt 0.56 0.58 0.59
## Duhachek 0.57 0.58 0.59
##
## Reliability if an item is dropped:
## raw_alpha std.alpha G6(smc) average_r S/N alpha se var.r med.r
## HBI_museum 0.52 0.53 0.51 0.14 1.1 0.0058 0.0048 0.14
## HBI_library 0.55 0.56 0.53 0.15 1.2 0.0055 0.0051 0.14
## HBI_scifair 0.54 0.54 0.51 0.14 1.2 0.0057 0.0032 0.15
## HBI_compute 0.55 0.55 0.53 0.15 1.2 0.0056 0.0054 0.15
## HBI_show 0.53 0.54 0.52 0.14 1.2 0.0057 0.0047 0.14
## HBI_fixed 0.58 0.58 0.55 0.16 1.4 0.0052 0.0044 0.15
## HBI_sciproj 0.55 0.55 0.52 0.15 1.2 0.0055 0.0032 0.15
## HBI_stemdisc 0.52 0.53 0.51 0.14 1.1 0.0059 0.0054 0.12
##
## Item statistics
## n raw.r std.r r.cor r.drop mean sd
## HBI_museum 15448 0.56 0.54 0.44 0.34 0.53 0.50
## HBI_library 15448 0.49 0.48 0.34 0.26 0.65 0.48
## HBI_scifair 15448 0.49 0.52 0.41 0.31 0.18 0.38
## HBI_compute 15448 0.44 0.49 0.35 0.27 0.86 0.35
## HBI_show 15448 0.53 0.52 0.40 0.30 0.63 0.48
## HBI_fixed 15448 0.44 0.42 0.25 0.18 0.45 0.50
## HBI_sciproj 15448 0.50 0.50 0.39 0.27 0.39 0.49
## HBI_stemdisc 15448 0.56 0.55 0.45 0.34 0.66 0.47
##
## Non missing response frequency for each item
## 0 1 miss
## HBI_museum 0.47 0.53 0
## HBI_library 0.35 0.65 0
## HBI_scifair 0.82 0.18 0
## HBI_compute 0.14 0.86 0
## HBI_show 0.37 0.63 0
## HBI_fixed 0.55 0.45 0
## HBI_sciproj 0.61 0.39 0
## HBI_stemdisc 0.34 0.66 0
#Rasch SPI
sbi_mod <- tam(sbi_vars)
## ....................................................
## Processing Data 2023-05-22 17:53:33.609525
## * Response Data: 15164 Persons and 8 Items
## * Numerical integration with 21 nodes
## * Created Design Matrices ( 2023-05-22 17:53:33.6479 )
## * Calculated Sufficient Statistics ( 2023-05-22 17:53:33.792006 )
## ....................................................
## Iteration 1 2023-05-22 17:53:33.819621
## E Step
## M Step Intercepts |----
## Deviance = 137978.9926
## Maximum item intercept parameter change: 0.324355
## Maximum item slope parameter change: 0
## Maximum regression parameter change: 0
## Maximum variance parameter change: 0.08542
## ....................................................
## Iteration 2 2023-05-22 17:53:33.898983
## E Step
## M Step Intercepts |---
## Deviance = 137187.0123 | Absolute change: 791.9803 | Relative change: 0.005773
## Maximum item intercept parameter change: 0.033164
## Maximum item slope parameter change: 0
## Maximum regression parameter change: 0
## Maximum variance parameter change: 0.123138
## ....................................................
## Iteration 3 2023-05-22 17:53:33.976086
## E Step
## M Step Intercepts |---
## Deviance = 137012.1325 | Absolute change: 174.8797 | Relative change: 0.00127638
## Maximum item intercept parameter change: 0.026825
## Maximum item slope parameter change: 0
## Maximum regression parameter change: 0
## Maximum variance parameter change: 0.10544
## ....................................................
## Iteration 4 2023-05-22 17:53:34.051767
## E Step
## M Step Intercepts |---
## Deviance = 136907.8556 | Absolute change: 104.277 | Relative change: 0.00076166
## Maximum item intercept parameter change: 0.021366
## Maximum item slope parameter change: 0
## Maximum regression parameter change: 0
## Maximum variance parameter change: 0.086303
## ....................................................
## Iteration 5 2023-05-22 17:53:34.141835
## E Step
## M Step Intercepts |--
## Deviance = 136848.1451 | Absolute change: 59.7105 | Relative change: 0.00043633
## Maximum item intercept parameter change: 0.016597
## Maximum item slope parameter change: 0
## Maximum regression parameter change: 0
## Maximum variance parameter change: 0.068231
## ....................................................
## Iteration 6 2023-05-22 17:53:34.225694
## E Step
## M Step Intercepts |--
## Deviance = 136814.9873 | Absolute change: 33.1578 | Relative change: 0.00024236
## Maximum item intercept parameter change: 0.012643
## Maximum item slope parameter change: 0
## Maximum regression parameter change: 0
## Maximum variance parameter change: 0.052526
## ....................................................
## Iteration 7 2023-05-22 17:53:34.296356
## E Step
## M Step Intercepts |--
## Deviance = 136796.9893 | Absolute change: 17.9981 | Relative change: 0.00013157
## Maximum item intercept parameter change: 0.00949
## Maximum item slope parameter change: 0
## Maximum regression parameter change: 0
## Maximum variance parameter change: 0.039633
## ....................................................
## Iteration 8 2023-05-22 17:53:34.368409
## E Step
## M Step Intercepts |--
## Deviance = 136787.3817 | Absolute change: 9.6076 | Relative change: 7.024e-05
## Maximum item intercept parameter change: 0.007046
## Maximum item slope parameter change: 0
## Maximum regression parameter change: 0
## Maximum variance parameter change: 0.029463
## ....................................................
## Iteration 9 2023-05-22 17:53:34.446174
## E Step
## M Step Intercepts |--
## Deviance = 136782.3149 | Absolute change: 5.0668 | Relative change: 3.704e-05
## Maximum item intercept parameter change: 0.005189
## Maximum item slope parameter change: 0
## Maximum regression parameter change: 0
## Maximum variance parameter change: 0.021666
## ....................................................
## Iteration 10 2023-05-22 17:53:34.523963
## E Step
## M Step Intercepts |--
## Deviance = 136779.666 | Absolute change: 2.6489 | Relative change: 1.937e-05
## Maximum item intercept parameter change: 0.0038
## Maximum item slope parameter change: 0
## Maximum regression parameter change: 0
## Maximum variance parameter change: 0.015806
## ....................................................
## Iteration 11 2023-05-22 17:53:34.587688
## E Step
## M Step Intercepts |--
## Deviance = 136778.2898 | Absolute change: 1.3762 | Relative change: 1.006e-05
## Maximum item intercept parameter change: 0.002771
## Maximum item slope parameter change: 0
## Maximum regression parameter change: 0
## Maximum variance parameter change: 0.011465
## ....................................................
## Iteration 12 2023-05-22 17:53:34.648226
## E Step
## M Step Intercepts |--
## Deviance = 136777.5779 | Absolute change: 0.7118 | Relative change: 5.2e-06
## Maximum item intercept parameter change: 0.002015
## Maximum item slope parameter change: 0
## Maximum regression parameter change: 0
## Maximum variance parameter change: 0.008282
## ....................................................
## Iteration 13 2023-05-22 17:53:34.72282
## E Step
## M Step Intercepts |--
## Deviance = 136777.2109 | Absolute change: 0.367 | Relative change: 2.68e-06
## Maximum item intercept parameter change: 0.001461
## Maximum item slope parameter change: 0
## Maximum regression parameter change: 0
## Maximum variance parameter change: 0.005965
## ....................................................
## Iteration 14 2023-05-22 17:53:34.801475
## E Step
## M Step Intercepts |--
## Deviance = 136777.0221 | Absolute change: 0.1888 | Relative change: 1.38e-06
## Maximum item intercept parameter change: 0.001058
## Maximum item slope parameter change: 0
## Maximum regression parameter change: 0
## Maximum variance parameter change: 0.004287
## ....................................................
## Iteration 15 2023-05-22 17:53:34.864779
## E Step
## M Step Intercepts |--
## Deviance = 136776.9252 | Absolute change: 0.097 | Relative change: 7.1e-07
## Maximum item intercept parameter change: 0.000765
## Maximum item slope parameter change: 0
## Maximum regression parameter change: 0
## Maximum variance parameter change: 0.003077
## ....................................................
## Iteration 16 2023-05-22 17:53:34.930214
## E Step
## M Step Intercepts |--
## Deviance = 136776.8754 | Absolute change: 0.0498 | Relative change: 3.6e-07
## Maximum item intercept parameter change: 0.000553
## Maximum item slope parameter change: 0
## Maximum regression parameter change: 0
## Maximum variance parameter change: 0.002206
## ....................................................
## Iteration 17 2023-05-22 17:53:34.988459
## E Step
## M Step Intercepts |--
## Deviance = 136776.8499 | Absolute change: 0.0255 | Relative change: 1.9e-07
## Maximum item intercept parameter change: 0.000399
## Maximum item slope parameter change: 0
## Maximum regression parameter change: 0
## Maximum variance parameter change: 0.00158
## ....................................................
## Iteration 18 2023-05-22 17:53:35.0714
## E Step
## M Step Intercepts |--
## Deviance = 136776.8368 | Absolute change: 0.0131 | Relative change: 1e-07
## Maximum item intercept parameter change: 0.000288
## Maximum item slope parameter change: 0
## Maximum regression parameter change: 0
## Maximum variance parameter change: 0.001131
## ....................................................
## Iteration 19 2023-05-22 17:53:35.156866
## E Step
## M Step Intercepts |--
## Deviance = 136776.8301 | Absolute change: 0.0067 | Relative change: 5e-08
## Maximum item intercept parameter change: 0.000207
## Maximum item slope parameter change: 0
## Maximum regression parameter change: 0
## Maximum variance parameter change: 0.00081
## ....................................................
## Iteration 20 2023-05-22 17:53:35.229729
## E Step
## M Step Intercepts |--
## Deviance = 136776.8267 | Absolute change: 0.0034 | Relative change: 3e-08
## Maximum item intercept parameter change: 0.00015
## Maximum item slope parameter change: 0
## Maximum regression parameter change: 0
## Maximum variance parameter change: 0.000579
## ....................................................
## Iteration 21 2023-05-22 17:53:35.305113
## E Step
## M Step Intercepts |--
## Deviance = 136776.8249 | Absolute change: 0.0018 | Relative change: 1e-08
## Maximum item intercept parameter change: 0.000108
## Maximum item slope parameter change: 0
## Maximum regression parameter change: 0
## Maximum variance parameter change: 0.000415
## ....................................................
## Iteration 22 2023-05-22 17:53:35.378687
## E Step
## M Step Intercepts |-
## Deviance = 136776.824 | Absolute change: 9e-04 | Relative change: 1e-08
## Maximum item intercept parameter change: 7.8e-05
## Maximum item slope parameter change: 0
## Maximum regression parameter change: 0
## Maximum variance parameter change: 0.000297
## ....................................................
## Iteration 23 2023-05-22 17:53:35.444228
## E Step
## M Step Intercepts |-
## Deviance = 136776.8236 | Absolute change: 5e-04 | Relative change: 0
## Maximum item intercept parameter change: 5.6e-05
## Maximum item slope parameter change: 0
## Maximum regression parameter change: 0
## Maximum variance parameter change: 0.000212
## ....................................................
## Iteration 24 2023-05-22 17:53:35.969366
## E Step
## M Step Intercepts |-
## Deviance = 136776.8233 | Absolute change: 2e-04 | Relative change: 0
## Maximum item intercept parameter change: 4e-05
## Maximum item slope parameter change: 0
## Maximum regression parameter change: 0
## Maximum variance parameter change: 0.000152
## ....................................................
## Iteration 25 2023-05-22 17:53:36.047893
## E Step
## M Step Intercepts |-
## Deviance = 136776.8232 | Absolute change: 1e-04 | Relative change: 0
## Maximum item intercept parameter change: 2.9e-05
## Maximum item slope parameter change: 0
## Maximum regression parameter change: 0
## Maximum variance parameter change: 0.000109
## ....................................................
## Iteration 26 2023-05-22 17:53:36.125925
## E Step
## M Step Intercepts |-
## Deviance = 136776.8231 | Absolute change: 1e-04 | Relative change: 0
## Maximum item intercept parameter change: 2.1e-05
## Maximum item slope parameter change: 0
## Maximum regression parameter change: 0
## Maximum variance parameter change: 7.8e-05
## ....................................................
## Item Parameters
## xsi.index xsi.label est
## 1 1 SBI_sch_mtg -2.0553
## 2 2 SBI_pto 0.6268
## 3 3 SBI_pt_conf -0.3639
## 4 4 SBI_sch_evnt -1.0321
## 5 5 SBI_volntr 1.0701
## 6 6 SBI_fundr -0.1653
## 7 7 SBI_counsl 0.3507
## 8 8 SBI_scifair 1.9891
## ...................................
## Regression Coefficients
## [,1]
## [1,] 0
##
## Variance:
## [,1]
## [1,] 1.668
##
##
## EAP Reliability:
## [1] 0.679
##
## -----------------------------
## Start: 2023-05-22 17:53:33.605284
## End: 2023-05-22 17:53:36.39581
## Time difference of 2.790526 secs
#Rasch HBI
hbi_mod <- tam(hbi_vars)
## ....................................................
## Processing Data 2023-05-22 17:53:36.666177
## * Response Data: 15448 Persons and 8 Items
## * Numerical integration with 21 nodes
## * Created Design Matrices ( 2023-05-22 17:53:36.708253 )
## * Calculated Sufficient Statistics ( 2023-05-22 17:53:36.744386 )
## ....................................................
## Iteration 1 2023-05-22 17:53:36.788514
## E Step
## M Step Intercepts |----
## Deviance = 144648.8513
## Maximum item intercept parameter change: 0.293136
## Maximum item slope parameter change: 0
## Maximum regression parameter change: 0
## Maximum variance parameter change: 0.044319
## ....................................................
## Iteration 2 2023-05-22 17:53:36.885336
## E Step
## M Step Intercepts |--
## Deviance = 144169.95 | Absolute change: 478.9013 | Relative change: 0.00332178
## Maximum item intercept parameter change: 0.009398
## Maximum item slope parameter change: 0
## Maximum regression parameter change: 0
## Maximum variance parameter change: 0.003765
## ....................................................
## Iteration 3 2023-05-22 17:53:36.988423
## E Step
## M Step Intercepts |--
## Deviance = 144167.4177 | Absolute change: 2.5324 | Relative change: 1.757e-05
## Maximum item intercept parameter change: 0.00551
## Maximum item slope parameter change: 0
## Maximum regression parameter change: 0
## Maximum variance parameter change: 0.003188
## ....................................................
## Iteration 4 2023-05-22 17:53:37.070857
## E Step
## M Step Intercepts |--
## Deviance = 144166.4793 | Absolute change: 0.9383 | Relative change: 6.51e-06
## Maximum item intercept parameter change: 0.003413
## Maximum item slope parameter change: 0
## Maximum regression parameter change: 0
## Maximum variance parameter change: 0.002594
## ....................................................
## Iteration 5 2023-05-22 17:53:37.148132
## E Step
## M Step Intercepts |--
## Deviance = 144166.1077 | Absolute change: 0.3716 | Relative change: 2.58e-06
## Maximum item intercept parameter change: 0.002154
## Maximum item slope parameter change: 0
## Maximum regression parameter change: 0
## Maximum variance parameter change: 0.002083
## ....................................................
## Iteration 6 2023-05-22 17:53:37.23102
## E Step
## M Step Intercepts |--
## Deviance = 144165.948 | Absolute change: 0.1597 | Relative change: 1.11e-06
## Maximum item intercept parameter change: 0.001387
## Maximum item slope parameter change: 0
## Maximum regression parameter change: 0
## Maximum variance parameter change: 0.001657
## ....................................................
## Iteration 7 2023-05-22 17:53:37.32549
## E Step
## M Step Intercepts |--
## Deviance = 144165.8732 | Absolute change: 0.0748 | Relative change: 5.2e-07
## Maximum item intercept parameter change: 0.000912
## Maximum item slope parameter change: 0
## Maximum regression parameter change: 0
## Maximum variance parameter change: 0.001308
## ....................................................
## Iteration 8 2023-05-22 17:53:37.418853
## E Step
## M Step Intercepts |--
## Deviance = 144165.8354 | Absolute change: 0.0379 | Relative change: 2.6e-07
## Maximum item intercept parameter change: 0.000612
## Maximum item slope parameter change: 0
## Maximum regression parameter change: 0
## Maximum variance parameter change: 0.001028
## ....................................................
## Iteration 9 2023-05-22 17:53:37.508382
## E Step
## M Step Intercepts |--
## Deviance = 144165.815 | Absolute change: 0.0204 | Relative change: 1.4e-07
## Maximum item intercept parameter change: 0.00042
## Maximum item slope parameter change: 0
## Maximum regression parameter change: 0
## Maximum variance parameter change: 0.000805
## ....................................................
## Iteration 10 2023-05-22 17:53:37.595398
## E Step
## M Step Intercepts |--
## Deviance = 144165.8035 | Absolute change: 0.0114 | Relative change: 8e-08
## Maximum item intercept parameter change: 0.000294
## Maximum item slope parameter change: 0
## Maximum regression parameter change: 0
## Maximum variance parameter change: 0.000628
## ....................................................
## Iteration 11 2023-05-22 17:53:37.68362
## E Step
## M Step Intercepts |--
## Deviance = 144165.7969 | Absolute change: 0.0066 | Relative change: 5e-08
## Maximum item intercept parameter change: 0.00021
## Maximum item slope parameter change: 0
## Maximum regression parameter change: 0
## Maximum variance parameter change: 0.000489
## ....................................................
## Iteration 12 2023-05-22 17:53:37.784236
## E Step
## M Step Intercepts |--
## Deviance = 144165.7931 | Absolute change: 0.0039 | Relative change: 3e-08
## Maximum item intercept parameter change: 0.000152
## Maximum item slope parameter change: 0
## Maximum regression parameter change: 0
## Maximum variance parameter change: 0.000381
## ....................................................
## Iteration 13 2023-05-22 17:53:37.886955
## E Step
## M Step Intercepts |--
## Deviance = 144165.7908 | Absolute change: 0.0023 | Relative change: 2e-08
## Maximum item intercept parameter change: 0.000111
## Maximum item slope parameter change: 0
## Maximum regression parameter change: 0
## Maximum variance parameter change: 0.000296
## ....................................................
## Iteration 14 2023-05-22 17:53:37.987137
## E Step
## M Step Intercepts |-
## Deviance = 144165.7894 | Absolute change: 0.0014 | Relative change: 1e-08
## Maximum item intercept parameter change: 8.3e-05
## Maximum item slope parameter change: 0
## Maximum regression parameter change: 0
## Maximum variance parameter change: 0.00023
## ....................................................
## Iteration 15 2023-05-22 17:53:38.091103
## E Step
## M Step Intercepts |-
## Deviance = 144165.7886 | Absolute change: 8e-04 | Relative change: 1e-08
## Maximum item intercept parameter change: 6.2e-05
## Maximum item slope parameter change: 0
## Maximum regression parameter change: 0
## Maximum variance parameter change: 0.000178
## ....................................................
## Iteration 16 2023-05-22 17:53:38.185621
## E Step
## M Step Intercepts |-
## Deviance = 144165.7881 | Absolute change: 5e-04 | Relative change: 0
## Maximum item intercept parameter change: 4.7e-05
## Maximum item slope parameter change: 0
## Maximum regression parameter change: 0
## Maximum variance parameter change: 0.000138
## ....................................................
## Iteration 17 2023-05-22 17:53:38.279009
## E Step
## M Step Intercepts |-
## Deviance = 144165.7878 | Absolute change: 3e-04 | Relative change: 0
## Maximum item intercept parameter change: 3.6e-05
## Maximum item slope parameter change: 0
## Maximum regression parameter change: 0
## Maximum variance parameter change: 0.000107
## ....................................................
## Iteration 18 2023-05-22 17:53:38.379704
## E Step
## M Step Intercepts |-
## Deviance = 144165.7876 | Absolute change: 2e-04 | Relative change: 0
## Maximum item intercept parameter change: 2.7e-05
## Maximum item slope parameter change: 0
## Maximum regression parameter change: 0
## Maximum variance parameter change: 8.3e-05
## ....................................................
## Item Parameters
## xsi.index xsi.label est
## 1 1 HBI_museum -0.1641
## 2 2 HBI_library -0.7273
## 3 3 HBI_scifair 1.8245
## 4 4 HBI_compute -2.1402
## 5 5 HBI_show -0.6472
## 6 6 HBI_fixed 0.2315
## 7 7 HBI_sciproj 0.5236
## 8 8 HBI_stemdisc -0.7958
## ...................................
## Regression Coefficients
## [,1]
## [1,] 0
##
## Variance:
## [,1]
## [1,] 0.9746
##
##
## EAP Reliability:
## [1] 0.578
##
## -----------------------------
## Start: 2023-05-22 17:53:36.662517
## End: 2023-05-22 17:53:38.694579
## Time difference of 2.032062 secs
# install.packages("WrightMap")
library(WrightMap)
IRT.WrightMap(sbi_mod)
IRT.WrightMap(hbi_mod)
home_involv <- cbind(data$P1MUSEUM, data$P1LIBRARY,
data$P1SCIFAIR, data$P1COMPUTER,
data$P1SHOW)
colnames(home_involv) <- c("HBI_museum","HBI_library",
"HBI_scifair",
"HBI_compute","HBI_show")
# Remove -9 and -8 from the dataset
home_involv[home_involv == -9 | home_involv == -8] <- NA
home_involv = na.omit(home_involv)
home_involv_reliability <- alpha(home_involv)
summary(home_involv_reliability)
##
## Reliability analysis
## raw_alpha std.alpha G6(smc) average_r S/N ase mean sd median_r
## 0.49 0.49 0.44 0.16 0.95 0.0063 0.57 0.25 0.15
home_involv_reliability
##
## Reliability analysis
## Call: alpha(x = home_involv)
##
## raw_alpha std.alpha G6(smc) average_r S/N ase mean sd median_r
## 0.49 0.49 0.44 0.16 0.95 0.0063 0.57 0.25 0.15
##
## 95% confidence boundaries
## lower alpha upper
## Feldt 0.48 0.49 0.51
## Duhachek 0.48 0.49 0.51
##
## Reliability if an item is dropped:
## raw_alpha std.alpha G6(smc) average_r S/N alpha se var.r med.r
## HBI_museum 0.39 0.39 0.32 0.14 0.63 0.0079 0.0011 0.15
## HBI_library 0.44 0.43 0.37 0.16 0.75 0.0071 0.0036 0.15
## HBI_scifair 0.47 0.47 0.40 0.18 0.87 0.0068 0.0027 0.16
## HBI_compute 0.47 0.47 0.41 0.18 0.89 0.0068 0.0022 0.16
## HBI_show 0.41 0.40 0.34 0.15 0.68 0.0075 0.0021 0.15
##
## Item statistics
## n raw.r std.r r.cor r.drop mean sd
## HBI_museum 15448 0.66 0.62 0.47 0.34 0.53 0.50
## HBI_library 15448 0.60 0.58 0.39 0.27 0.65 0.48
## HBI_scifair 15448 0.49 0.53 0.31 0.22 0.18 0.38
## HBI_compute 15448 0.46 0.53 0.29 0.21 0.86 0.35
## HBI_show 15448 0.63 0.60 0.44 0.31 0.63 0.48
##
## Non missing response frequency for each item
## 0 1 miss
## HBI_museum 0.47 0.53 0
## HBI_library 0.35 0.65 0
## HBI_scifair 0.82 0.18 0
## HBI_compute 0.14 0.86 0
## HBI_show 0.37 0.63 0
home_sch_conf <- cbind(data$P1FIXED,
data$P1SCIPROJ,data$P1STEMDISC)
colnames(home_sch_conf) <- c("HBI_fixed", "HBI_sciproj",
"HBI_stemdisc")
home_sch_conf[home_sch_conf == -9 | home_sch_conf == -8] <- NA
home_sch_conf = na.omit(home_sch_conf)
home_sch_conf_reliability <- alpha(home_sch_conf)
summary(home_sch_conf_reliability)
##
## Reliability analysis
## raw_alpha std.alpha G6(smc) average_r S/N ase mean sd median_r
## 0.33 0.33 0.25 0.14 0.49 0.0094 0.5 0.32 0.15
home_sch_conf_reliability
##
## Reliability analysis
## Call: alpha(x = home_sch_conf)
##
## raw_alpha std.alpha G6(smc) average_r S/N ase mean sd median_r
## 0.33 0.33 0.25 0.14 0.49 0.0094 0.5 0.32 0.15
##
## 95% confidence boundaries
## lower alpha upper
## Feldt 0.31 0.33 0.35
## Duhachek 0.31 0.33 0.35
##
## Reliability if an item is dropped:
## raw_alpha std.alpha G6(smc) average_r S/N alpha se var.r med.r
## HBI_fixed 0.25 0.25 0.15 0.15 0.34 0.012 NA 0.15
## HBI_sciproj 0.30 0.30 0.18 0.18 0.43 0.011 NA 0.18
## HBI_stemdisc 0.18 0.18 0.10 0.10 0.22 0.013 NA 0.10
##
## Item statistics
## n raw.r std.r r.cor r.drop mean sd
## HBI_fixed 15448 0.66 0.65 0.32 0.18 0.45 0.50
## HBI_sciproj 15448 0.64 0.64 0.28 0.16 0.39 0.49
## HBI_stemdisc 15448 0.66 0.67 0.38 0.22 0.66 0.47
##
## Non missing response frequency for each item
## 0 1 miss
## HBI_fixed 0.55 0.45 0
## HBI_sciproj 0.61 0.39 0
## HBI_stemdisc 0.34 0.66 0
# install.packages("lavaan")
# install.packages("lavaanPlot")
library(lavaan)
## This is lavaan 0.6-15
## lavaan is FREE software! Please report any bugs.
##
## Attaching package: 'lavaan'
## The following object is masked from 'package:psych':
##
## cor2cov
library(lavaanPlot)
model <- 'hi =~ HBI_museum + HBI_library + HBI_scifair + HBI_compute + HBI_show
hsc =~ HBI_fixed + HBI_sciproj + HBI_stemdisc'
hbi_fit <- cfa(model, data = hbi_vars)
summary(hbi_fit, standardized = TRUE, ci = TRUE,
fit.measures = TRUE)
## lavaan 0.6.15 ended normally after 50 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 17
##
## Number of observations 15448
##
## Model Test User Model:
##
## Test statistic 1851.839
## Degrees of freedom 19
## P-value (Chi-square) 0.000
##
## Model Test Baseline Model:
##
## Test statistic 8531.222
## Degrees of freedom 28
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.784
## Tucker-Lewis Index (TLI) 0.682
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -73894.447
## Loglikelihood unrestricted model (H1) -72968.527
##
## Akaike (AIC) 147822.893
## Bayesian (BIC) 147952.862
## Sample-size adjusted Bayesian (SABIC) 147898.837
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.079
## 90 Percent confidence interval - lower 0.076
## 90 Percent confidence interval - upper 0.082
## P-value H_0: RMSEA <= 0.050 0.000
## P-value H_0: RMSEA >= 0.080 0.303
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.050
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## hi =~
## HBI_museum 1.000 1.000 1.000
## HBI_library 0.746 0.027 28.110 0.000 0.694 0.798
## HBI_scifair 0.631 0.022 29.133 0.000 0.589 0.673
## HBI_compute 0.517 0.019 27.356 0.000 0.480 0.554
## HBI_show 0.895 0.029 30.946 0.000 0.838 0.952
## hsc =~
## HBI_fixed 1.000 1.000 1.000
## HBI_sciproj 1.373 0.068 20.222 0.000 1.240 1.506
## HBI_stemdisc 1.734 0.081 21.530 0.000 1.576 1.892
## Std.lv Std.all
##
## 0.236 0.473
## 0.176 0.369
## 0.149 0.391
## 0.122 0.353
## 0.211 0.438
##
## 0.132 0.265
## 0.181 0.371
## 0.229 0.483
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## hi ~~
## hsc 0.029 0.001 20.962 0.000 0.026 0.031
## Std.lv Std.all
##
## 0.922 0.922
##
## Variances:
## Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
## .HBI_museum 0.193 0.003 69.614 0.000 0.188 0.199
## .HBI_library 0.197 0.003 78.065 0.000 0.192 0.202
## .HBI_scifair 0.123 0.002 76.559 0.000 0.120 0.126
## .HBI_compute 0.105 0.001 79.009 0.000 0.102 0.107
## .HBI_show 0.188 0.003 72.923 0.000 0.183 0.193
## .HBI_fixed 0.230 0.003 82.384 0.000 0.225 0.236
## .HBI_sciproj 0.206 0.003 75.398 0.000 0.200 0.211
## .HBI_stemdisc 0.172 0.003 60.506 0.000 0.166 0.178
## hi 0.056 0.002 22.659 0.000 0.051 0.061
## hsc 0.017 0.001 12.219 0.000 0.015 0.020
## Std.lv Std.all
## 0.193 0.776
## 0.197 0.864
## 0.123 0.847
## 0.105 0.875
## 0.188 0.808
## 0.230 0.930
## 0.206 0.863
## 0.172 0.767
## 1.000 1.000
## 1.000 1.000
lavaanPlot(model = hbi_fit, node_options = list(shape = "box",
fontname = "Helvetica"),
edge_options = list(color = "grey"),
coefs = T, stand = T, covs = T)