The family of missing Hull student, Libby Squire, have pleaded with the 21-year-old to get in touch as the search for her continues into its fourth day.

Her parents, Lisa and Russell Squire, released a statement asking for information about “our kind, thoughtful, beautiful girl” as officers said they were keeping an open mind about the circumstances surrounding her disappearance.

Libby Squire. Photograph: PA

“Libby, my darling pie, we just want to know that you are safe,” said the student’s mother, her voice breaking with emotion as she spoke. “Please get in touch with us any way you can. The whole family is missing you, especially me and your dad, your sisters and your brother. I miss you so much it’s breaking my heart not knowing where you are. I love you.”

Her father said she was “loved by so many people” and appealed for anyone with any information to come forward “no matter how small or irrelevant it may be”. Speaking directly to his daughter, who has not been seen since late on Thursday night, he said: “We just want you home.”

The statement was filmed and released by Humberside police. Ch Supt Phil Ward said that officers had found Libby’s mobile phone at her home, but it had not yielded any more information about her movements.

She was reported missing after getting into a taxi outside Hull’s Welly club on Beverley Road at about 11pm on Thursday. Police believe she had completed the journey of about a mile back to the vicinity of her home on Wellesley Avenue by about 11.30pm, but she did not go inside.

Ch Supt Phil Ward (pictured) said officers had found Libby Squire’s mobile phone at her home. Photograph: Peter Byrne/PA

A motorist helped her shortly afterwards and has since come forward to help police with their search. Libby Squire was last seen on CCTV at about 11.45pm near the junction of Beverley Road and Haworth Street, round the corner from her home.

On Monday, officers were searching the area. On Wellesley Avenue, officers were searching drains and wheelie bins, while detectives conducted door-to-door inquiries on Haworth Street. Officers from the police marine unit travelled along a length of the frozen Beverley and Barmston Drain in inflatable rafts, breaking the ice and searching the water.

Ward said her parents were “distressed and anxious” but said the force was keeping an open mind. “While the investigation has been treated as a missing person inquiry, we have always, and will continue to, keep an open mind as to the circumstances surrounding Libby’s disappearance,” he said. “While her location is not yet known, this does not mean she has come to harm but we must carry out a thorough investigation and explore all possibilities.”

Police urged anyone living in the area to check their gardens and outbuildings in case she has taken shelter from the cold weather. Anyone who was driving around the area between 11pm on Thursday and 3am on Friday and has dashcam footage was also asked to come forward by contacting 101.

Ryan Tweddell, a friend of Libby who organised a search by about 200 students on Saturday, said: “Libby is a loving, down-to-earth, typical, normal student. She is hardworking, helps everyone who needs it and is a lovely, brilliant girl.”