├── .gitignore ├── examples ├── irt-model.jbl ├── irt-item-coef.jbl ├── test_scores.py ├── test_lsat6_2pl.py └── lsat6.dat ├── test ├── resource │ ├── demo-irt-model.jbl │ └── demo-irt-item-coef.jbl └── irt_3pl_demo.py ├── README.md ├── src ├── irt_simulator.py └── irt.py └── LICENSE /.gitignore: -------------------------------------------------------------------------------- 1 | .idea 2 | __pycache__ -------------------------------------------------------------------------------- /examples/irt-model.jbl: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/binhetech/irt-rpy/master/examples/irt-model.jbl -------------------------------------------------------------------------------- /examples/irt-item-coef.jbl: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/binhetech/irt-rpy/master/examples/irt-item-coef.jbl -------------------------------------------------------------------------------- /test/resource/demo-irt-model.jbl: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/binhetech/irt-rpy/master/test/resource/demo-irt-model.jbl -------------------------------------------------------------------------------- /test/resource/demo-irt-item-coef.jbl: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/binhetech/irt-rpy/master/test/resource/demo-irt-item-coef.jbl -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | # irt-rpy 2 | 3 | 基于Item Response Theory(irt)项目反应理论，封装R语言的IRT库进行试题(item)参数估计、能力(theta)参数估计。 4 | 5 | # 简介 6 | 7 | + 支持根据专家经验直接设置试题参数创建IRT模型 8 | + 支持基于答题记录(response pattern)进行试题、能力参数联合估计 9 | + 单维IRT模型支持Rasch, 2PL, 3PL, 4PL等模型 10 | + 已知试题参数，估计能力参数 11 | + 已知试题参数，模拟答题记录 12 | 13 | # 功能 14 | 15 | # 使用 16 | 17 | ## 依赖 18 | 19 | + R语言环境(>=3.6.3) 20 | + R包mirt 21 | + R包mirtCAT 22 | 23 | # 致谢 24 | 25 | ## mirt 26 | 27 | https://github.com/philchalmers/mirt 28 | 29 | ## mirtCAT 30 | 31 | https://github.com/philchalmers/mirtCAT -------------------------------------------------------------------------------- /test/irt_3pl_demo.py: -------------------------------------------------------------------------------- 1 | #!/usr/bin/env python 2 | # -*- coding: utf-8 -*- 3 | # @Time : 2021/4/16 15:42 4 | # @Author : hebin 5 | # @File : irt_3pl_demo.py 6 | import sys 7 | 8 | import json 9 | import joblib 10 | import numpy as np 11 | import pandas as pd 12 | 13 | sys.path.append("../") 14 | 15 | from src.irt import IRTModel 16 | 17 | 18 | def irt_3pl_demo(): 19 | # 模拟答题矩阵 20 | datas = pd.DataFrame(np.random.randint(0, 2, (1000, 10))) 21 | print("data shape={}".format(datas.shape)) 22 | irt = IRTModel(10, model=None, model_save_path="./resource/demo-irt-model.jbl", 23 | item_para_save_path="./resource/demo-irt-item-coef.jbl") 24 | irt.fit(datas, dims=1, itemtype="3PL", method="EM") 25 | irt.calc_coef(IRTpars="F") 26 | irt.extract_items_match_thetas() 27 | 28 | 29 | if __name__ == "__main__": 30 | irt_3pl_demo() 31 | -------------------------------------------------------------------------------- /examples/test_scores.py: -------------------------------------------------------------------------------- 1 | #!/usr/bin/env python 2 | # -*- coding: utf-8 -*- 3 | # @Time : 2021/4/16 16:01 4 | # @Author : hebin 5 | # @File : test_scores.py 6 | import sys 7 | 8 | import numpy as np 9 | import pandas as pd 10 | 11 | sys.path.append("../") 12 | 13 | from src.irt import IRTModel 14 | 15 | 16 | def test_scores(): 17 | datas = pd.DataFrame({"item_0": [0, 1, 1, 0, 1, 0, 1], 18 | "item_1": [0, 0, 1, 1, 1, 0, 1], 19 | "item_2": [0, 0, 1, 1, 1, 0, 1], 20 | "item_3": [0, 1, 1, 0, 1, 0, 1], 21 | "item_4": [0, 1, 1, 0, 1, 0, 1], 22 | }) 23 | print("data shape={}".format(datas.shape)) 24 | irt = IRTModel(5, model=None, model_save_path="./irt-model.jbl", 25 | item_para_save_path="./irt-item-coef.jbl") 26 | irt.fit(datas, dims=1, itemtype="Rasch", method="EM") 27 | irt.calc_scores("MAP", datas.values, True) 28 | 29 | response_pattern = np.array([np.nan, np.nan, np.nan, np.nan, 1]) 30 | irt.calc_scores("MAP", response_pattern, True) 31 | 32 | response_pattern = np.array([np.nan, np.nan, np.nan, np.nan, 1]) 33 | irt.calc_scores("MAP", response_pattern, True) 34 | 35 | response_pattern = np.array([np.nan, np.nan, np.nan, 0, 1]) 36 | irt.calc_scores("MAP", response_pattern, True) 37 | 38 | response_pattern = np.array([np.nan, np.nan, 0, 0, 1]) 39 | irt.calc_scores("MAP", response_pattern, True) 40 | 41 | response_pattern = np.array([np.nan, 0, 0, 0, 1]) 42 | irt.calc_scores("MAP", response_pattern, True) 43 | 44 | response_pattern = np.array([[np.nan, 0, 0, 0, 1], [0, 0, 0, 0, 1]]) 45 | irt.calc_scores("MAP", response_pattern, True) 46 | 47 | 48 | if __name__ == "__main__": 49 | test_scores() 50 | -------------------------------------------------------------------------------- /examples/test_lsat6_2pl.py: -------------------------------------------------------------------------------- 1 | #!/usr/bin/env python 2 | # -*- coding: utf-8 -*- 3 | # @Time : 2021/4/16 15:45 4 | # @Author : hebin 5 | # @File : test_lsat6_2pl.py 6 | import sys 7 | 8 | import numpy as np 9 | import pandas as pd 10 | 11 | sys.path.append("../") 12 | 13 | from src.irt import IRTModel 14 | 15 | 16 | def test_lsat6(): 17 | # A data frame with the responses of 1000 individuals to 5 questions 18 | data = open("../examples/lsat6.dat", "r", encoding="utf-8").readlines() 19 | datas = pd.DataFrame() 20 | for it, i in enumerate(data): 21 | cols = i.strip().split("\t") 22 | cols = [int(i) for i in cols] 23 | datas = datas.append(pd.DataFrame([pd.Series(cols).add_prefix("item_")]), ignore_index=True) 24 | print("data shape={}".format(datas.shape)) 25 | irt = IRTModel(5, model=None, model_save_path="./irt-model.jbl", item_para_save_path="./irt-item-coef.jbl") 26 | # 试题、能力参数联合估计 27 | irt.fit(datas, dims=1, itemtype="2PL", method="EM") 28 | irt.calc_coef(IRTpars="F") 29 | # 能力参数估计 30 | scores = irt.calc_scores() 31 | print("scores={}".format(scores)) 32 | for i, p in enumerate(irt.item_paras): 33 | print("item {} paras: {}".format(i, p)) 34 | 35 | 36 | def test_lsat6_na(): 37 | # A data frame with the responses of 1000 individuals to 5 questions 38 | data = open("../examples/lsat6.dat", "r", encoding="utf-8").readlines() 39 | datas = pd.DataFrame() 40 | for it, i in enumerate(data): 41 | cols = i.strip().split("\t") 42 | cols = [int(i) for i in cols] 43 | if it == 0: 44 | # 答题数据缺失时，用np.nan填充 45 | cols = [0, 1, np.nan, 1, 1] 46 | datas = datas.append(pd.DataFrame([pd.Series(cols).add_prefix("item_")]), ignore_index=True) 47 | print("data shape={}".format(datas.shape)) 48 | 49 | # 答题数据缺失时 50 | datas.iloc[0]["item_1"] = np.nan 51 | datas.iloc[3]["item_2"] = np.nan 52 | 53 | irt = IRTModel(5, model=None, model_save_path="./irt-model.jbl", item_para_save_path="./irt-item-coef.jbl") 54 | # 试题、能力参数联合估计 55 | irt.fit(datas, dims=1, itemtype="2PL", method="EM") 56 | irt.calc_coef(IRTpars="F") 57 | for i, p in enumerate(irt.item_paras): 58 | print("item {} paras: {}".format(i, p)) 59 | 60 | 61 | if __name__ == "__main__": 62 | test_lsat6() 63 | test_lsat6_na() 64 | -------------------------------------------------------------------------------- /src/irt_simulator.py: -------------------------------------------------------------------------------- 1 | #!/usr/bin/env python 2 | # -*- coding: utf-8 -*- 3 | # @Time : 2021/4/12 19:26 4 | # @Author : hebin 5 | # @File : irt_simulator.py 6 | import joblib 7 | import json 8 | import numpy as np 9 | 10 | from irt import IRTModel 11 | 12 | 13 | class IRTSimulator(object): 14 | """ 15 | 利用IRT理论进行自适应学习题目推荐效果评估. 16 | """ 17 | 18 | def __init__(self, item_num, model_save_path, item_index_path, item_para_save_path): 19 | model = joblib.load(open(model_save_path, "rb")) 20 | self.model = IRTModel(item_num, model, model_save_path=model_save_path, item_para_save_path=item_para_save_path) 21 | self.item_index = joblib.load(open(item_index_path, "rb")) 22 | self.item_responses = [np.nan for _ in range(item_num)] 23 | self.problem_id2item_id = {str(v): k for k, v in enumerate(self.item_index)} 24 | print("IRT simulator loaded (item num={})".format(len(self.problem_id2item_id))) 25 | 26 | def get_response_patterns(self, problem_seq, result_seq): 27 | value = self.item_responses[:] 28 | for p, a in zip(problem_seq, result_seq): 29 | if str(p) in self.problem_id2item_id: 30 | value[self.problem_id2item_id[str(p)]] = a 31 | return value 32 | 33 | def evaluate_theta(self, responses, method="EAP"): 34 | if len([i for i in responses if not np.isnan(i)]) == 0: 35 | return -1, -1, 0 36 | try: 37 | status = 0 38 | assert len(responses) == len(self.item_responses) 39 | theta = self.model.calc_scores(method, np.array(responses))[0][0] 40 | # 能力值归一化 41 | score = self.model.normalization(theta) 42 | except Exception: 43 | status = -1 44 | theta = -1 45 | score = 0 46 | return status, theta, score 47 | 48 | def get_item_prob_answers(self, theta, cur_problem_seq): 49 | answers = [] 50 | for i in cur_problem_seq: 51 | if str(i) in self.problem_id2item_id: 52 | # 基于当前能力估计答题概率 53 | item_id = self.problem_id2item_id[str(i)] 54 | ans = self.model.get_item_expected_value(item_id, theta) 55 | ans = 0 if ans < 0.5 else 1 56 | answers.append(ans) 57 | else: 58 | answers.append(0) 59 | return answers 60 | 61 | def evaluate_ep(self, history_problem_seq, history_result_seq, recommend_topic_seq, method="predict"): 62 | try: 63 | history_response_patterns = self.get_response_patterns(history_problem_seq, history_result_seq) 64 | # 估计历史答题记录的能力 65 | status, theta, Es = self.evaluate_theta(history_response_patterns) 66 | if status < 0: 67 | return status, 0 68 | cur_problem_seq = history_problem_seq + recommend_topic_seq 69 | if method == "predict": 70 | # 基于能力估计预测答题正确的概率，生成答题结果 71 | answers = self.get_item_prob_answers(theta, recommend_topic_seq) 72 | else: 73 | # 构造老师答题结果 74 | answers = [1 for i in recommend_topic_seq] 75 | cur_result_seq = history_result_seq + answers 76 | cur_response_patterns = self.get_response_patterns(cur_problem_seq, cur_result_seq) 77 | status, cur_theta, Ee = self.evaluate_theta(cur_response_patterns) 78 | if status < 0: 79 | return status, 0 80 | Ep = (Ee - Es) / (1 - Es) 81 | except Exception: 82 | status = -1 83 | Ep = -1 84 | return status, Ep 85 | -------------------------------------------------------------------------------- /src/irt.py: -------------------------------------------------------------------------------- 1 | #!/usr/bin/env python 2 | # -*- coding: utf-8 -*- 3 | # @Time : 2021/2/24 15:11 4 | # @Author : hebin 5 | # @File : irt.py 6 | 7 | 8 | import joblib 9 | import time 10 | import numpy as np 11 | 12 | # python call R 13 | import rpy2.robjects as ro 14 | from rpy2.robjects.packages import importr 15 | from rpy2.robjects import pandas2ri, numpy2ri 16 | 17 | # activate 18 | pandas2ri.activate() 19 | numpy2ri.activate() 20 | 21 | # import package 22 | mirt = importr('mirt') 23 | mirtCAT = importr('mirtCAT') 24 | 25 | 26 | class IRTModel(object): 27 | 28 | def __init__(self, item_num, model=None, model_save_path="./resource/irt-model.jbl", 29 | item_para_save_path="./resource/irt-item-coef.jbl"): 30 | """ 31 | IRT类初始化. 32 | 33 | Args: 34 | item_num: int, 题库中试题数量 35 | model: int, 已估计完成的irt模型文件，使用joblib存储 36 | model_save_path: string, 估计模型后模型保存路径 37 | item_para_save_path: string, 估计模型后试题参数保存路径 38 | 39 | """ 40 | 41 | self.student_num = 0 42 | self.item_num = item_num 43 | # list of numpy.array 44 | self.item_paras = [] 45 | self.item_obj = [object] * item_num 46 | # 当前试题匹配的能力theta 47 | self.item_thetas = [] 48 | self.model_save_path = model_save_path 49 | self.item_para_save_path = item_para_save_path 50 | 51 | # 加载已完成参数估计的模型对象文件 52 | self.model = model 53 | if model is not None: 54 | # 已估计的模型参数重计算 55 | self.calc_coef() 56 | # 计算每道试题对应的最佳匹配能力值 57 | self.extract_items_match_thetas() 58 | 59 | def define_irt_model(self, data, itemtype="3PL", save=True): 60 | """ 61 | 根据人工经验设置irt参数(如3PL: a, d, g, u)来定义模型. 62 | 63 | Args: 64 | data: np.array, 已设置好的试题参数， 65 | item_1: a1, d, g, u 66 | item_2: a1, d, g, u 67 | ... 68 | itemtype: string, 模型类型， "3PL", "2PL" 69 | 70 | Returns: 71 | 72 | """ 73 | data = np.array(data) 74 | # 更新试题参数 75 | self.item_num = data.shape[0] 76 | # 需要对R变量赋值 77 | ro.r.assign("pars", numpy2ri.py2rpy(data)) 78 | self.model = ro.r("generate.mirt_object(pars, '%s')" % itemtype) 79 | if save: 80 | with open(self.model_save_path, "wb") as f: 81 | joblib.dump(self.model, f) 82 | print("{} model saved to {}".format(itemtype, self.model_save_path)) 83 | return self.model 84 | 85 | def simdata(self, num): 86 | """ 87 | 模拟答题数据response patterns. 88 | 89 | Args: 90 | num: int, 返回数据个数 91 | 92 | Returns: 93 | 94 | """ 95 | # 需要对R变量赋值 96 | ro.r.assign("model", self.model) 97 | # 运行R函数 98 | data = ro.r("simdata(model=model, N=%d)" % num) 99 | return data 100 | 101 | def fit(self, data, dims=1, itemtype="3PL", method="EM", save=True): 102 | """ 103 | 基于答题/响应数据进行IRT模型参数估计. 104 | 105 | Args: 106 | data: pandas.DataFrame, 行是学生，列是题目(item0, item1, item2, ...) 107 | dims: mirt.model模型对象或数字指示维度大小, 单维项目反映理论设置为1 108 | itemtype: 项目参数类型，包括'Rasch', '2PL', '3PL', '3PLu', '4PL'. 109 | Form must be: (discrimination, difficulty, lower-bound, upper-bound) 110 | method: "EM", "MCEM" 111 | save: boolean, 是否保存模型对象文件 112 | 113 | Returns: 114 | 115 | """ 116 | t_start = time.time() 117 | self.student_num, self.item_num = data.shape 118 | # pandas.DataFrame to R objects 119 | data = pandas2ri.py2rpy(data) 120 | # 需要对R变量赋值 121 | ro.r.assign("data", data) 122 | # 运行R函数 123 | self.model = ro.r( 124 | "mirt(data,model=%d,itemtype='%s',method='%s',removeEmptyRows=TRUE)" % (dims, itemtype, method)) 125 | print("{} model fit completed, elapsed time={}".format(itemtype, time.time() - t_start)) 126 | if save: 127 | with open(self.model_save_path, "wb") as f: 128 | joblib.dump(self.model, f) 129 | print("IRT model saved to {}".format(self.model_save_path)) 130 | 131 | def calc_coef(self, IRTpars="F", save=True): 132 | """ 133 | 计算已拟合模型的项目item参数. 134 | 135 | Args: 136 | IRTpars: string, 是否转换为原始IRT参数 137 | save: boolean, 是否保存参数文件 138 | 139 | Returns: 140 | 141 | """ 142 | t_start = time.time() 143 | ro.r.assign("model", self.model) 144 | coef = ro.r("paras <- coef(model, as.data.frame=F, IRTpars=%s)" % IRTpars) 145 | coef = coef[:self.item_num] 146 | self.item_paras = [i[0] for i in coef] 147 | self.item_obj = [object] * self.item_num 148 | if save: 149 | with open(self.item_para_save_path, "wb") as f: 150 | joblib.dump(self.item_paras, f) 151 | # print("coef calculated completed. time={}".format(time.time() - t_start)) 152 | return self.item_paras 153 | 154 | def normalization(self, x): 155 | """ 156 | 难度值b归一化. 157 | y = exp(x)/(1+exp(x)) 158 | x = log(y/(1-y)) 159 | 160 | Args: 161 | x: 162 | 163 | Returns: 164 | 165 | """ 166 | return np.exp(x) / (np.exp(x) + 1) 167 | 168 | def calc_scores(self, method="EAP", response_pattern=None, verbose=False): 169 | """ 170 | 已知试题参数，估计被试者的能力分数. 171 | 172 | Args: 173 | method: string, "EAP", "MAP", "ML" 174 | response_pattern: numpy, 答题结果，注意shape == item_nun, 如果为None, 则返回原模型的估计能力值 175 | 176 | Returns: 177 | scores: list of [f1 score, standard error] 178 | 179 | """ 180 | t_start = time.time() 181 | ro.r.assign("model", self.model) 182 | if response_pattern is not None: 183 | # print(response_pattern) 184 | rp = numpy2ri.py2rpy(response_pattern) 185 | ro.r.assign("response_pattern", rp) 186 | scores = ro.r( 187 | "fscores(model, method='%s', full.scores=TRUE, full.scores.SE=TRUE, response.pattern=response_pattern, append_response.pattern=FALSE)" % method) 188 | else: 189 | scores = ro.r( 190 | "fscores(model, method='%s', full.scores=TRUE, full.scores.SE=TRUE)" % method) 191 | if verbose: 192 | print("{} ability estimate {} completed, time={}, theta={}".format(method, len(scores.tolist()), 193 | time.time() - t_start, scores)) 194 | return scores 195 | 196 | def extract_items_match_thetas(self): 197 | """ 198 | 提取试题匹配的能力值. 199 | """ 200 | item_thetas = [] 201 | for i, p in enumerate(self.item_paras): 202 | self.item_obj[i] = self.extract_item(i) 203 | theta = self.extract_item_theta(self.item_obj[i]) 204 | item_thetas.append(theta) 205 | self.item_thetas = np.array(item_thetas) 206 | return self.item_thetas 207 | 208 | def extract_item(self, item_id): 209 | """ 210 | 根据试题id提取item对象. 211 | 212 | Args: 213 | item_id: 214 | 215 | Returns: 216 | 217 | """ 218 | ro.r.assign("model", self.model) 219 | ro.r.assign("item", item_id + 1) 220 | # R语言中数组是以1开始的 221 | extra = ro.r("extract.item(model, item, group=NULL, drop.zeros = FALSE)") 222 | return extra 223 | 224 | def get_item_info(self, item_id, theta): 225 | ro.r.assign("x", self.item_obj[item_id]) 226 | ro.r.assign("Theta", theta) 227 | value = ro.r("iteminfo(x, Theta, degrees = NULL, total.info = TRUE, multidim_matrix = FALSE)") 228 | return value 229 | 230 | def get_items_info(self, cur_theta): 231 | values = [[i, abs(self.item_thetas[i] - cur_theta)] for i, p in enumerate(self.item_paras)] 232 | return values 233 | 234 | def get_item_expected_value(self, item_id, theta): 235 | ro.r.assign("x", self.item_obj[item_id]) 236 | ro.r.assign("Theta", theta) 237 | value = ro.r("expected.item(x, Theta)") 238 | return value 239 | 240 | def extract_item_theta(self, x): 241 | ro.r.assign("x", x) 242 | theta = np.arange(-6, 6.01, 0.01) 243 | ro.r.assign("Theta", theta) 244 | value = ro.r("iteminfo(x, Theta, degrees = NULL, total.info = TRUE, multidim_matrix = FALSE)") 245 | value = [(i, j) for i, j in zip(theta, value)] 246 | # 计算最大信息对应的theta 247 | theta = sorted(value, key=lambda i: i[1], reverse=True)[0][0] 248 | return theta 249 | -------------------------------------------------------------------------------- /LICENSE: -------------------------------------------------------------------------------- 1 | Apache License 2 | Version 2.0, January 2004 3 | http://www.apache.org/licenses/ 4 | 5 | TERMS AND CONDITIONS FOR USE, REPRODUCTION, AND DISTRIBUTION 6 | 7 | 1. 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